# How do you simplify (c^3)^4?

Oct 2, 2016

${c}^{12}$

#### Explanation:

While there is a law of indices which we could use, let's use basics.

${x}^{4} \text{ means } x \times x \times x \times x$

In the same way ${\left({c}^{3}\right)}^{4} \text{ means } {c}^{3} \times {c}^{3} \times {c}^{3} \times {c}^{3}$

The bases are all the same, so add the indices to get ${c}^{12}$

A quicker method is using the power law :${\left({x}^{m}\right)}^{n} = {x}^{m \times n}$

"raising a power to another power, times the indices"

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