Question

Apply the product rule of integer exponents to find the numerical equivalent of 12−5⋅127%0D%0A12%0D%0A−%0D%0A5%0D%0A⋅%0D%0A12%0D%0A7%0D%0A. Show your work and explain how you used the product rule of integer exponents.(2 points

Answer 1

We have 12^(−5) · 12^7. The product rule for integer exponents says a^m · a^n = a^(m+n) when the bases are the same. Here m = −5 and n = 7, so

12^(−5) · 12^7 = 12^(−5+7) = 12^2 = 144.

(You can also see this by writing 12^(−5) = 1/12^5, then (1/12^5)·12^7 = 12^(7−5) = 12^2 = 144.)