Problem: What would the result be if instead of raising 5 to the 4th power, you raised the number 4 to the 4th power?

InternLM-Math Base 20B:

  Reasoning: 4^4 = <<4^4=4*4*4*4=256>>256.
### Answer: 256

Expected answer: 256

Correct? Yes

Problem: What would the outcome be if we raise 6 to the power of 3, instead of 9?

InternLM-Math Base 20B:

  Reasoning: 6^3 = <<6^3=216>>216
### Answer: 216

Expected answer: 216

Correct? Yes

Problem: What is the value if we are cubing 7 instead of 5?

InternLM-Math Base 20B:

  Reasoning: 7^3 = <<7^3=343>>343
### Answer: 343

Expected answer: 343

Correct? Yes

Problem: What would be the result if we raise 8 to the power of 2 instead of 9?

InternLM-Math Base 20B:

  Reasoning: 8^2 = <<8^2=64>>64
### Answer: 64

Expected answer: 64

Correct? Yes

Problem: In the previous problem, you found the value of 3 to the power of 3. Now, consider what would happen if the base was 5 instead of 3. What is the value of 5 to the power of 3?

InternLM-Math Base 20B:

  5^3 = <<5^3=125>>125

Expected answer: 125

Correct? Yes

Problem: Considering our previous problem, if instead of 9 we raise 4 to the power of 2, what would be the value?

InternLM-Math Base 20B:

  Reasoning: 4^2 = <<4^2=16>>16
### Answer: 16

Expected answer: 16

Correct? Yes

Problem: After learning about the calculation of 9^2, can you now tell me what is the result of 7^2?

InternLM-Math Base 20B:

  7^2 = <<7^2=49>>49

Expected answer: 49

Correct? Yes

Problem: If we changed the base in the previous question to 4 while keeping the exponent as 3, what value would we get for 4^3?

InternLM-Math Base 20B:

  4^3 = <<4^3=64>>64
### Answer: 64

Expected answer: 64

Correct? Yes

Problem: What would the value be if instead of 6, we have 4 squared or 4^2?

InternLM-Math Base 20B:

  Reasoning: 4^2 = 4*4 = <<4*4=16>>16
### Answer: 16

Expected answer: 16

Correct? Yes

Problem: In the previous problem, we found the cube of 3. Now, what would be the value if we raise 6 to the power of 3 instead?

InternLM-Math Base 20B:

  Reasoning: 6^3 = <<6^3=216>>216
### Answer: 216

Expected answer: 216

Correct? Yes

Problem: What happens if we instead consider 4 raised to the power of 2?

InternLM-Math Base 20B:

  Reasoning: 4^2 = <<4^2=16>>16
### Answer: 16

Expected answer: 16

Correct? Yes

Problem: Earlier, we found out the value for 9 raised to the third power, right? Now, considering the same scenario, what would be the value if you raise 5 instead of 9 to the power of 3?

InternLM-Math Base 20B:

  Reasoning: 5^3 = <<5^3=125>>125
### Answer: 125

Expected answer: 125

Correct? Yes

Problem: In the previous situation we evaluated the square of 2. Now, consider what would the value be if instead of 2, we needed to evaluate the square of 5?

InternLM-Math Base 20B:

  5^2 = <<5^2=25>>25

Expected answer: 25

Correct? Yes

Problem: Following the previous question, what would be the value if we raised the number 2 to the power of 2 instead of 7?

InternLM-Math Base 20B:

  Reasoning: 2^2 = <<2^2=4>>4
### Answer: 4

Expected answer: 4

Correct? Yes

Problem: In the previous problem, we evaluated 8 raised to the power of 3. What if we changed the base and considered 7 instead of 8? What is the value of 7 raised to the power of 3?

InternLM-Math Base 20B:

  7^3 = <<7^3=343>>343

Expected answer: 343

Correct? Yes

Problem: Now, what if instead you were to calculate the square of 8? What would be the value of 8^2?

InternLM-Math Base 20B:

  Reasoning: 8^2 = <<8^2=64>>64.
### Answer: 64

Expected answer: 64

Correct? Yes

Problem: What would be the result if instead of raising 9 to the power of 2, we raised 6 to the power of 2?

InternLM-Math Base 20B:

  Reasoning: 6^2 = <<6^2=36>>36
### Answer: 36

Expected answer: 36

Correct? Yes

Problem: What is the value if we consider a cube with a side length of 8 units instead of 5 units?

InternLM-Math Base 20B:

  Reasoning: 8 cubed = 8 x 8 x 8 = <<8*8*8=512>>512
### Answer: 512

Expected answer: 512

Correct? Yes

Problem: What is the outcome when 4 is raised to the power of 2, instead of 5?

InternLM-Math Base 20B:

  Reasoning: 4^2 = <<4^2=16>>16
### Answer: 16

Expected answer: 16

Correct? Yes

Problem: Following from the previous problem, what would be the value if we raised 8 to the power of 2 instead of 5?

InternLM-Math Base 20B:

  Reasoning: 8^2 = <<8^2=64>>64
### Answer: 64

Expected answer: 64

Correct? Yes

Problem: You previously calculated 2 raised to the power of 3. Now, what would be the result if we raise 10 to the power of 3 instead?

InternLM-Math Base 20B:

 10^3 = <<10^3=1000>>1000

Expected answer: 1000

Correct? Yes

Problem: Given what you have learned, what happens if you take the new number 3 and raise it to the power of 3 instead?

InternLM-Math Base 20B:

  3^3 = <<3^3=27>>27

Expected answer: 27

Correct? Yes

Problem: What would the result be if we change the exponent from 9 to 6 and compute the value of 1 raised to the power of 6 instead?

InternLM-Math Base 20B:

  Reasoning: 1^6 = <<1^6=1>>1
### Answer: 1

Expected answer: 1

Correct? Yes

Problem: Previously, we raised 8 to the power of 3. Now, what if we raise 5 to the power of 3, what would be the result?

InternLM-Math Base 20B:

  5^3 = <<5^3=125>>125

Expected answer: 125

Correct? Yes

Problem: Given the understanding that 1 raised to the power of 2 gives us 1, what would be the result if we raised 4 to the power of 2 instead?

InternLM-Math Base 20B:

  Reasoning: 4^2 = <<4^2=16>>16
### Answer: 16

Expected answer: 16

Correct? Yes

Problem: Previously, you evaluated 2^2. Now, what's the result of performing an identical operation, but instead of squared (2^2), it is raised to the 7th power (2^7)?

InternLM-Math Base 20B:

  2^7 = <<2^7=128>>128

Expected answer: 128

Correct? Yes

Problem: What would be the result if we took one instead of eight and raised it to the power of 2?

InternLM-Math Base 20B:

  Reasoning: 1^2 = <<1^2=1>>1
### Answer: 1

Expected answer: 1

Correct? Yes

Problem: What would the result be if you raised 7 to the power of 3 instead of 2 in the previous problem?

InternLM-Math Base 20B:

  7^3 = <<7^3=343>>343

Expected answer: 343

Correct? Yes

Problem: What would be the value if you squared 1 instead of 8?

InternLM-Math Base 20B:

  1^2 = <<1^2=1>>1

Expected answer: 1

Correct? Yes

Problem: Following the previous problem, what would be the result if we evaluate 6 to the power of 1 instead of 3?

InternLM-Math Base 20B:

  6^1 = <<6^1=6>>6

Expected answer: 6

Correct? Yes

Problem: Now, consider what will be the value when 7 is not just raised to the power of 1, but to the power of 3 instead?

InternLM-Math Base 20B:

  7^3 = <<7^3=343>>343

Expected answer: 343

Correct? Yes

Problem: In the previous problem, you found the result of 2 raised to the power of 2. Now, what is the result of 4 raised to the power of 2?

InternLM-Math Base 20B:

  Reasoning: 4 raised to the power of 2 = <<4^2=16>>16.
### Answer: 16

Expected answer: 16

Correct? Yes

Problem: Following up on our previous question, what would be the result if we raised 10, instead of 4, to the power of 2?

InternLM-Math Base 20B:

 10^2 = <<10^2=100>>100

Expected answer: 100

Correct? Yes

Problem: What would be the value if instead of 9^2, we calculated 4^2?

InternLM-Math Base 20B:

  Reasoning: 4^2 = <<4^2=16>>16
### Answer: 16

Expected answer: 16

Correct? Yes

Problem: What is the value if we consider raising 7 to the power of 3 instead of 5^3?

InternLM-Math Base 20B:

  Reasoning: 7^3 = 7*7*7 = <<7*7*7=343>>343
### Answer: 343

Expected answer: 343

Correct? Yes

Problem: What would be the result if instead of raising 7 to the power of 3, you raised 9 to the power of 3?

InternLM-Math Base 20B:

  Reasoning: 9^3 = <<9^3=729>>729
### Answer: 729

Expected answer: 729

Correct? Yes

Problem: Suppose instead of 2 units, you only had a single unit. What would be the result if you squared that single unit (1^2)?

InternLM-Math Base 20B:

  1^2 = <<1^2=1>>1

Expected answer: 1

Correct? Yes

Problem: Now imagine if we raised 3 to the power of 3 instead, what would be the result?

InternLM-Math Base 20B:

  3^3 = <<3^3=27>>27

Expected answer: 27

Correct? Yes

Problem: In the previous problem, we evaluated 2^3. Now consider if it were 3^3 instead. What value would that give?

InternLM-Math Base 20B:

  3^3 = <<3^3=27>>27

Expected answer: 27

Correct? Yes

Problem: What would the value be if we have 6^3 instead of 7^3?

InternLM-Math Base 20B:

  Reasoning: 6^3 = 6*6*6 = <<6*6*6=216>>216
### Answer: 216

Expected answer: 216

Correct? Yes

Problem: What is the result if we have 8 groups, not 10, of spiders, each group having a power of 2?

InternLM-Math Base 20B:

  Reasoning: 2^8 = 2*2*2*2*2*2*2*2 = <<2*2*2*2*2*2*2*2=256>>256
### Answer: 256

Expected answer: 64

Correct? No

Problem: What if, instead of 1, the base was changed to 6? What would be the result of 6 raised to the power of 2?

InternLM-Math Base 20B:

  Reasoning: 6^2 = <<6^2=36>>36
### Answer: 36

Expected answer: 36

Correct? Yes

Problem: Now consider this: What would be the result if we were to raise 7 to the power of 3 instead of 9? Calculate 7^3.

InternLM-Math Base 20B:

  7^3 = <<7^3=343>>343
### Answer: 343

Expected answer: 343

Correct? Yes

Problem: What is 3^2? In other words, if now you're considering 3 instances of a number being multiplied by itself instead of the single instance we previously evaluated, what would the new result be?

InternLM-Math Base 20B:

  Reasoning: 3^2 = <<3^2=9>>9
### Answer: 9

Expected answer: 9

Correct? Yes

Problem: What would the result be if we now consider 1 raised to the power 2 instead of 2 raised to the power 2?

InternLM-Math Base 20B:

  Reasoning: 1 raised to the power 2 = 1^2 = <<1^2=1>>1.
### Answer: 1

Expected answer: 1

Correct? Yes

Problem: What happens to the result when instead of squaring 4, you square 7?

InternLM-Math Base 20B:

  Reasoning: 7 squared = 7*7 = <<7*7=49>>49
### Answer: 49

Expected answer: 49

Correct? Yes

Problem: What would be the result if we raise 8 instead of 7 to the power of 3?

InternLM-Math Base 20B:

  8^3 = <<8^3=512>>512

Expected answer: 512

Correct? Yes

Problem: Following the previous question, consider that instead of taking 4^3, we take 5^3. What is now the value?

InternLM-Math Base 20B:

 5^3 = <<5^3=125>>125

Expected answer: 125

Correct? Yes

Problem: What would be the value if you raised 7 to the power of 2 instead of 1?

InternLM-Math Base 20B:

  Reasoning: 7^2 = <<7^2=49>>49.
### Answer: 49

Expected answer: 49

Correct? Yes

Problem: Suppose you originally had 3 square blocks instead of 6. What is the result of squaring the number of these blocks now, i.e., what is 3^2?

InternLM-Math Base 20B:

  3^2 = <<3^2=9>>9

Expected answer: 9

Correct? Yes

Problem: In the previous problem, we calculated the square of 2. But what if we had 3 instead of 2 to begin with? What would be the result of 3 raised to the power of 2?

InternLM-Math Base 20B:

  Reasoning: 3 raised to the power of 2 = <<3^2=9>>9.
### Answer: 9

Expected answer: 9

Correct? Yes

Problem: Now, consider what will be the value if instead of 4, we square 9? What will 9^2 be?

InternLM-Math Base 20B:

  9^2 = <<9^2=81>>81

Expected answer: 81

Correct? Yes

Problem: Following the previous problem, what if, instead of 3, we raised 8 to the power of 2? What would be the value?

InternLM-Math Base 20B:

  Reasoning: 8^2 = <<8^2=64>>64.
### Answer: 64

Expected answer: 64

Correct? Yes

Problem: What would be the result if we change the base number from 10 to 9, and compute 9 raised to the power of 3?

InternLM-Math Base 20B:

  Reasoning: 9^3 = <<9^3=729>>729
### Answer: 729

Expected answer: 729

Correct? Yes

Problem: Following our previous calculation, let's change the numbers a bit. What's the value now if we evaluate 10^1?

InternLM-Math Base 20B:

  10^1 = <<10^1=10>>10

Expected answer: 10

Correct? Yes

Problem: What if instead of elevating 7 to the power of 3, we changed the base and elevated 2 to the power of 3? What would be the result then?

InternLM-Math Base 20B:

  2^3 = <<2^3=8>>8

Expected answer: 8

Correct? Yes

Problem: What happens if we consider 6 instead of 2 and raise it to the power of 2?

InternLM-Math Base 20B:

  Reasoning: 6 raised to the power of 2 = <<6^2=36>>36.
### Answer: 36

Expected answer: 36

Correct? Yes

Problem: Next, consider what happens if instead of 5, we have 4 in the base. What would be the new value if 4 is raised to the power of 3?

InternLM-Math Base 20B:

  4^3 = <<4^3=64>>64

Expected answer: 64

Correct? Yes

Problem: Consider the original finding where we raised 5 to the power of 4. Now, what would be the result if we raised 1 to the power of 4 instead?

InternLM-Math Base 20B:

  Reasoning: 1^4 = <<1^4=1*1*1*1=1>>1
### Answer: 1

Expected answer: 1

Correct? Yes

Problem: Considering the previous problem where we calculated 3^5, what would be the result if we instead calculated 2^5?

InternLM-Math Base 20B:

  Reasoning: 2^5 = <<2^5=32>>32
### Answer: 32

Expected answer: 32

Correct? Yes

Problem: What would be the result if we raised 5 to the power of 2 instead of 2?

InternLM-Math Base 20B:

 5^2 = <<5^2=25>>25

Expected answer: 25

Correct? Yes

Problem: What would be the value if originally, instead of 4^2, it was calculated as 9^2?

InternLM-Math Base 20B:

  Reasoning: 9^2 = <<9^2=9*9=81>>81
### Answer: 81

Expected answer: 81

Correct? Yes

Problem: What would be the value if we considered 7^2 instead of 6^2?

InternLM-Math Base 20B:

  7^2 = <<7^2=49>>49
### Answer: 49

Expected answer: 49

Correct? Yes

Problem: What is the result if we replace the base number from the previous problem (which was 10), with 7? In other words, what is the value of 7^3?

InternLM-Math Base 20B:

  Reasoning: 7^3 = <<7^3=343>>343
### Answer: 343

Expected answer: 343

Correct? Yes

Problem: Following up from your last computation, how would the outcome change if you raised 6 to the power of 2 instead of 4?

InternLM-Math Base 20B:

  Reasoning: 6 ^ 2 = <<6^2=36>>36
### Answer: 36

Expected answer: 36

Correct? Yes

Problem: What would be the outcome if instead of 10, we raised 1 to the power of 3?

InternLM-Math Base 20B:

  Reasoning: 1^3 = <<1^3=1>>1
### Answer: 1

Expected answer: 1

Correct? Yes

Problem: Following up from the previous question, what would the result be if we raised 3 to the power of 3 instead of 7?

InternLM-Math Base 20B:

  Reasoning: 3^3 = <<3^3=27>>27
### Answer: 27

Expected answer: 27

Correct? Yes

Problem: What would the result be if instead of raising 8 to the power of 2, we raised 7 to the power of 2?

InternLM-Math Base 20B:

  7^2 = <<7^2=49>>49

Expected answer: 49

Correct? Yes

Problem: What would be the result if instead of cubing 7, you cubed 6?

InternLM-Math Base 20B:

  Reasoning: 6^3 = <<6^3=216>>216
### Answer: 216

Expected answer: 216

Correct? Yes

Problem: Considering the same calculation, what is the result if we raise 6 to the power of 2 instead of 8?

InternLM-Math Base 20B:

  6^2 = <<6^2=36>>36

Expected answer: 36

Correct? Yes

Problem: Previously, you computed the value of 2 raised to the power 3. Now, calculate what happens if you raise 5 to the power 3 instead.

InternLM-Math Base 20B:

  5^3 = <<5^3=125>>125

Expected answer: 125

Correct? Yes

Problem: In continuation of the previous problem, now calculate the value of 4 raised to the power of 2.

InternLM-Math Base 20B:

  4^2 = <<4^2=16>>16

Expected answer: 16

Correct? Yes

Problem: What would happen if instead of 7, we raised 10 to the power of 2?

InternLM-Math Base 20B:

  Reasoning: 10^2 = <<10^2=100>>100
### Answer: 100

Expected answer: 100

Correct? Yes

Problem: Now consider what happens if instead of raising 10 to the power of 2, we instead raise 2 to the power of 2. What would be the value?

InternLM-Math Base 20B:

  2^2 = <<2^2=4>>4

Expected answer: 4

Correct? Yes

Problem: What would be the value if you raise 9 to the power of 2 instead of 6?

InternLM-Math Base 20B:

  9^2 = <<9^2=81>>81
### Answer: 81

Expected answer: 81

Correct? Yes

Problem: What would be the result if, instead of 3, we raised 5 to the power of 3?

InternLM-Math Base 20B:

  Reasoning: 5^3 = 5*5*5 = <<5*5*5=125>>125
### Answer: 125

Expected answer: 125

Correct? Yes

Problem: What would be the result if we raised 9 to the power of 3 instead of 1?

InternLM-Math Base 20B:

  Reasoning: 9^3 = <<9^3=729>>729
### Answer: 729

Expected answer: 729

Correct? Yes

Problem: What would be the value if we instead raised 3 to the power of 1?

InternLM-Math Base 20B:

  3^1 = <<3^1=3>>3

Expected answer: 3

Correct? Yes

Problem: Following the previous problem, what would be the result if we consider 3 raised to the power of 1?

InternLM-Math Base 20B:

  Reasoning: 3^1 = 3
### Answer: 3

Expected answer: 3

Correct? Yes

Problem: What is the result if instead of cubic value of 8, we calculate the cubic value of 1, expressed as 1^3?

InternLM-Math Base 20B:

  1^3 = <<1^3=1*1*1=1>>1
### Answer: 1

Expected answer: 1

Correct? Yes

Problem: Following our previous calculation of 9^2, let's change the number. What is the value of 5^2?

InternLM-Math Base 20B:

  5^2 = <<5^2=25>>25

Expected answer: 25

Correct? Yes

Problem: What is the result if the base 2 is raised to the power of 1 instead of 2?

InternLM-Math Base 20B:

  Reasoning: 2 to the power of 1 = <<2^1=2>>2.
### Answer: 2

Expected answer: 2

Correct? Yes

Problem: If we reconsider the previous concept but instead use 3 as the base, what would be the value of 3 squared?

InternLM-Math Base 20B:

  3 squared is 3 times 3, which is 9.

Expected answer: 9

Correct? Yes

Problem: What is the square of 7?

InternLM-Math Base 20B:

  7^2 = <<7^2=49>>49

Expected answer: 49

Correct? Yes

Problem: In the previous problem, you calculated the value when 8 was raised to the power of 3. What would the value be if instead we raise 7 to the power of 3?

InternLM-Math Base 20B:

  7^3 = <<7^3=343>>343

Expected answer: 343

Correct? Yes

Problem: What happens if we change the situation a bit and instead of 3, we use 2 and raise it to the power of 3? What would be the result?

InternLM-Math Base 20B:

  Reasoning: 2^3 = <<2^3=8>>8
### Answer: 8

Expected answer: 8

Correct? Yes

Problem: What would the cube be if we considered 3 instead of 9?

InternLM-Math Base 20B:

  Reasoning: 3^3 = <<3^3=27>>27
### Answer: 27

Expected answer: 27

Correct? Yes

Problem: In the previous problem, you found the result of raising 9 to the third power. Now, what if instead of raising 9, you raise 3 to the third power? What would be the result then?

InternLM-Math Base 20B:

  Reasoning: 3^3 = <<3^3=27>>27
### Answer: 27

Expected answer: 27

Correct? Yes

Problem: "What would be the result if instead of raising 6 to the power of 3, we raised 10 to the power of 3?"

InternLM-Math Base 20B:

 10^3 = <<10^3=1000>>1000

Expected answer: 1000

Correct? Yes

Problem: What would the result be if we squared a smaller number, like 4^2?

InternLM-Math Base 20B:

  Reasoning: 4^2 = 4*4 = <<4*4=16>>16
### Answer: 16

Expected answer: 16

Correct? Yes

Problem: Continuing from the previous question, what would be the value if instead of 8 raised to the power of 2, we now have 10 raised to the power of 2?

InternLM-Math Base 20B:

  10^2 = <<10^2=100>>100

Expected answer: 100

Correct? Yes

Problem: Based on the previous problem, let's consider a different scenario. What will be the value when 2 raised to the power of 3 instead of 10?

InternLM-Math Base 20B:

  2^3 = <<2^3=8>>8

Expected answer: 8

Correct? Yes

Problem: Now reflect on the previous problem but this time think about what would happen if it was 7 that was raised to the power of 3. What would be the value then?

InternLM-Math Base 20B:

  Reasoning: 7^3 = <<7^3=343>>343
### Answer: 343

Expected answer: 343

Correct? Yes

Problem: What would be the result if there was only 1 number instead of 7, and it was raised to the power of 3?

InternLM-Math Base 20B:

  Reasoning: 1^3 = 1*1*1 = <<1*1*1=1>>1
### Answer: 1

Expected answer: 1

Correct? Yes

Problem: In the previous problem, we evaluated what happens when 5 is raised to the power of 3. Now, suppose we had started with 2 instead of 5. What would be the result if 2 were raised to the power of 3?

InternLM-Math Base 20B:

  2^3 = <<2^3=8>>8

Expected answer: 8

Correct? Yes

Problem: Following on from the previous question, what would the outcome be if we replaced 7 with 9 in our exponent calculation? In other words, what is the value of 9^3?

InternLM-Math Base 20B:

  Reasoning: 9^3 = 9*9*9 = <<9*9*9=729>>729
### Answer: 729

Expected answer: 729

Correct? Yes

Problem: What would be the result if 1 is raised to the 9th power instead of the 5th power?

InternLM-Math Base 20B:

  1^9 = <<1^9=1>>1

Expected answer: 1

Correct? Yes