Question

write me a paragraph and explain my work

apply the product rule of integer exponents to find the numerical equivalent of 12 to the power of -5 times 12 to the pwoer of 7

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the numerical value of the expression 12 to the power of -5 times 12 to the power of 7, we can apply the product rule of integer exponents. According to this rule, when multiplying two numbers with the same base, we add their exponents. In this case, the base is 12. So, by adding the exponents -5 and 7, we get a total exponent of 2. Therefore, 12 to the power of -5 times 12 to the power of 7 simplifies to 12 raised to the power of 2, which is equal to 144.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To apply the product rule of integer exponents to find the numerical equivalent of 12 to the power of -5 times 12 to the power of 7, we can combine the two terms using the rule that states when multiplying exponential expressions with the same base, we add the exponents. In this case, 12 to the power of -5 multiplied by 12 to the power of 7 can be simplified as 12 raised to the power of (-5 + 7) which is 12 to the power of 2. Thus, the numerical equivalent of 12 to the power of -5 times 12 to the power of 7 is 12 to the power of 2, which equals 144.

Answer 3

[AI-generated answer — Explain Bot]

To find the numerical value of 12 to the power of -5 multiplied by 12 to the power of 7 using the product rule of integer exponents, we need to understand the rule and apply it correctly. The product rule states that when multiplying two numbers that have the same base, we add their exponents. In this case, the base is 12, and we have -5 as the exponent for the first term and 7 as the exponent for the second term. To find the result, we add the exponents -5 and 7 together, which gives us 2. Therefore, the numerical equivalent of 12 to the power of -5 times 12 to the power of 7 is 12 to the power of 2, which can be calculated as 12 x 12, resulting in 144.