Question

Which expression is equivalent to 12 to the 10 over 12?

Answer 1

Answer:  Choice C

Work Shown:

$\frac{12^{10}}{12}\\\\\\\frac{12^{10}}{12^1}\\\\\\12^{10-1}\\\\\\12^{9}\\\\\\\frac{1}{12^{-9}}\\\\\\\left(\frac{1}{12}\right)^{-9}$

In the third step, I used the rule that $\frac{a^b}{a^c} = a^{b-c}$. You subtract the exponents when dividing exponents of the same base.

After that, I used the rule $a^{-b} = \frac{1}{a^b}$ which is the same as saying $a^{b} = \frac{1}{a^{-b}}$ to end up with choice C as the answer.