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 you multiply two numbers with the same base, you can add their exponents.

To find the numerical equivalent of 12^-5 * 12^7, we first apply the product rule by adding the exponents of 12. The base is the same, which is 12.

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

Next, we simplify the exponent:

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

Finally, we calculate the numerical value of 12^2, which is:
12^2 = 144

Therefore, 12^-5 * 12^7 is equal to 144.