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

Mar 2, 2018

You have to follow exponent laws in order to find the answer.

#### Explanation:

${\left({x}^{3}\right)}^{4}$
Becomes:

${x}^{3 \cdot 4}$

$= {x}^{12}$

Mar 2, 2018

The answer is ${x}^{12}$.

#### Explanation:

Write out the whole power of $4$, then add up the exponents using the exponent addition rule. I color-coded some of the problem so that it is easier to see:

$\textcolor{w h i t e}{=} {\left({x}^{3}\right)}^{4}$

$= \left({x}^{\textcolor{red}{3}}\right) \left({x}^{\textcolor{y e l l o w}{3}}\right) \left({x}^{\textcolor{g r e e n}{3}}\right) \left({x}^{\textcolor{b l u e}{3}}\right)$

$= {x}^{\textcolor{red}{3}} \cdot {x}^{\textcolor{y e l l o w}{3}} \cdot {x}^{\textcolor{g r e e n}{3}} \cdot {x}^{\textcolor{b l u e}{3}}$

$= {x}^{\textcolor{red}{3} + \textcolor{y e l l o w}{3}} \cdot {x}^{\textcolor{g r e e n}{3}} \cdot {x}^{\textcolor{b l u e}{3}}$

$= {x}^{\textcolor{\mathmr{and} a n \ge}{6}} \cdot {x}^{\textcolor{g r e e n}{3}} \cdot {x}^{\textcolor{b l u e}{3}}$

$= {x}^{\textcolor{\mathmr{and} a n \ge}{6} + \textcolor{g r e e n}{3}} \cdot {x}^{\textcolor{b l u e}{3}}$

$= {x}^{\textcolor{b r o w n}{9}} \cdot {x}^{\textcolor{b l u e}{3}}$

$= {x}^{\textcolor{b r o w n}{9} + \textcolor{b l u e}{3}}$

$= {x}^{12}$