# How do you simplify (x^6)^3/(x^4)^6?

Aug 28, 2016

$\frac{1}{x} ^ 6$

#### Explanation:

Using the $\textcolor{b l u e}{\text{laws of exponents}}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder}}$

• color(red)(|bar(ul(color(white)(a/a)color(black)((a^m)^n=a^mn)color(white)(a/a)|)))

$\Rightarrow {\left({x}^{6}\right)}^{3} = {x}^{6 \times 3} = {x}^{18} \text{ and } {\left({x}^{4}\right)}^{6} = {x}^{4 \times 6} = {x}^{24}$

Thus we have ${\left({x}^{6}\right)}^{3} / {\left({x}^{4}\right)}^{6} = {x}^{18} / {x}^{24}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\frac{{a}^{m}}{{a}^{n}} = {a}^{m - n}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\Rightarrow \frac{{x}^{18}}{{x}^{24}} = {x}^{18 - 24} = {x}^{- 6}$

$\textcolor{\mathmr{and} a n \ge}{\text{Reminder }} \textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{{a}^{- m} = \frac{1}{{a}^{m}}} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\Rightarrow {x}^{- 6} = \frac{1}{x} ^ 6$
$\textcolor{b l u e}{\text{-------------------------------------------------------------}}$

$\Rightarrow {\left({x}^{6}\right)}^{3} / {\left({x}^{4}\right)}^{6} = \frac{{x}^{18}}{x} ^ \left(24\right) = {x}^{- 6} = \frac{1}{x} ^ 6$