Question

apply the product rule of integer exponents to find the numerical equivalent to 12 to the power of -5 times 12 to the power of 7. show your work and explain how you used the product rule of integer exponents.

Answer 1

The product rule of integer exponents states that when multiplying two numbers with the same base, we add the exponents.

First, let's rewrite 12 to the power of -5 as 1/12^5.

So, we have (1/12^5) * 12^7.

Now, using the product rule of integer exponents, we add the exponents to get 12^7-5.

12^7-5 = 12^2.

Therefore, the numerical equivalent is 12^2, which is equal to 144.