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.

Answer 1

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

In this problem, we have 12 raised to the power of -5 multiplied by 12 raised to the power of 7. Since the base is the same (12), we can apply the product rule of integer exponents.

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

Now, we can calculate the sum of the exponents:

12^(-5 + 7) = 12^2

Since 12 raised to the power of 2 is equal to 144, the numerical equivalent of 12^-5 x 12^7 is 144.