# How do you fill in the blank for the expression (c^4)^?=c^12?

Oct 11, 2015

${\left({c}^{4}\right)}^{3} = {c}^{12}$

#### Explanation:

This comes from the following rule for exponents

${\left({x}^{n}\right)}^{m} = {x}^{n m}$

${c}^{4} = \left(c\right) \left(c\right) \left(c\right) \left(c\right)$
${\left[\left(c\right) \left(c\right) \left(c\right) \left(c\right)\right]}^{3} = \left[\left(c\right) \left(c\right) \left(c\right) \left(c\right)\right] \left[\left(c\right) \left(c\right) \left(c\right) \left(c\right)\right] \left[\left(c\right) \left(c\right) \left(c\right) \left(c\right)\right]$
There are $12$ or ${c}^{12}$, count them.