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. Reminder, you are looking for a numerical equivalent for this problem. Explain how you got your answer.
To find the numerical equivalent of 12^-5.12^7, we can simplify it by using the product rule of integer exponents, which states that when two numbers with the same base are multiplied, we can add their exponents.
In this case, we have 12^-5 multiplied by 12^7.
We can rewrite 12 as 2 * 2 * 3, so our expression becomes:
(2 * 2 * 3)^-5 * (2 * 2 * 3)^7
Now we can apply the product rule by adding the exponents:
(2 * 2 * 3)^(-5+7)
Simplifying further:
(2 * 2 * 3)^2
This is equal to (4 * 3)^2 which is (12)^2.
Therefore, the numerical equivalent of 12^-5.12^7 is 12^2 or 144.
To summarize, we used the product rule of integer exponents to add the exponents of two numbers with the same base (12), resulting in the simplification of the expression to 12^2 or 144.