Question

Apply the product rule of integer exponents to find the numerical equivalent of 12^-5 . 12^7. Show your work and explain how you used the product rule of integer exponents.(2 points)

Answer 1

The product rule of integer exponents states that when you multiply two numbers with the same base raised to different exponents, you can add the exponents together.

To find the numerical equivalent of 12^-5 . 12^7, we can apply the product rule of integer exponents.

First, let's simplify the expression by adding the exponents:

12^-5 . 12^7 = 12^(-5+7)

Next, we add the exponents: -5 + 7 = 2

So, 12^-5 . 12^7 is equivalent to 12^2.

To find the numerical equivalent, we can calculate 12^2:

12^2 = 12 * 12 = 144

Therefore, the numerical equivalent of 12^-5 . 12^7 is 144.

We used the product rule of integer exponents by adding the exponents of the same base (12) together.