apply the product rule of integer exponents to find the numerical equivalent of 12^-15 ⋅ 12^7. Show your work and explain how you used the product rule of integer exponents

Answer 1

To apply the product rule of integer exponents, we need to add the exponents when multiplying two numbers with the same base.

The product rule states:
a^m ⋅ a^n = a^(m + n)

Let's simplify the expression 12^-15 ⋅ 12^7 using the product rule:

12^-15 ⋅ 12^7 = 12^(-15 + 7)

Next, we add the exponents:
-15 + 7 = -8

Therefore, 12^-15 ⋅ 12^7 equals 12^-8.

Explanation:
By applying the product rule of integer exponents, we added the exponents -15 and 7 to get -8. We can now represent 12^-15 ⋅ 12^7 as 12^-8.