Question

Question
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

To apply the product rule of integer exponents, we need to add the exponents when multiplying two numbers with the same base.

The product rule of integer exponents states that for any nonzero number a and positive integers m and n, a^m * a^n = a^(m+n).

In this case, we have 12^(-5) * 12^7.

First, let's simplify 12^(-5):

12^(-5) = 1 / 12^5 = 1 / (12 * 12 * 12 * 12 * 12) = 1 / 248,832

Now, let's apply the product rule of integer exponents:

12^(-5) * 12^7 = (1 / 248,832) * 12^7 = 12^(7-5) / 248,832 = 12^2 / 248,832

Finally, let's calculate the numerical value:

12^2 = 12 * 12 = 144

Therefore, the numerical equivalent of 12^(-5) * 12^7 is 144 / 248,832, which can be further simplified if necessary.