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.
The product rule of integer exponents states that when multiplying two numbers with the same base raised to different exponents, we can add the exponents.
In this case, we have 12^-5 multiplied by 12^7. To apply the product rule of integer exponents, we add the exponents together:
12^(-5 + 7)
= 12^2
= 144
Therefore, the numerical equivalent of 12^-5 • 12^7 is 144.
We used the product rule of integer exponents by adding the exponents together because we have the same base, which is 12, raised to different exponents (-5 and 7) in the expression.