# How do you simplify ((-7^2 r^5 s^-3)/( 3^-1 r^-4 s^4))^4?

Jul 11, 2015

$A = \frac{\left({147}^{4}\right) \cdot {r}^{36}}{{s}^{28}}$

#### Explanation:

Let's go to simplify : $A = {\left(\frac{- {7}^{2} {r}^{5} {s}^{- 3}}{{3}^{- 1} {r}^{- 4} {s}^{4}}\right)}^{4}$

First, use this properties :
$\to$$\textcolor{red}{{a}^{- n} = \frac{1}{a} ^ n}$
$\to$$\textcolor{red}{\frac{1}{a} ^ \left(- n\right) = {a}^{n}}$

$A = {\left(\frac{- {7}^{2} \cdot \textcolor{red}{{3}^{1}} {r}^{5} \textcolor{red}{{r}^{4}}}{{s}^{4} \textcolor{red}{{s}^{3}}}\right)}^{4}$

Second, simplify $A$ with that :

$\textcolor{b l u e}{{a}^{n} \cdot {a}^{m} = {a}^{n + m}}$

$A = {\left(\frac{- 49 \cdot 3 \cdot \textcolor{b l u e}{{r}^{9}}}{\textcolor{b l u e}{{s}^{7}}}\right)}^{4}$

Finally, apply the power $4$ to the fraction inside the parenthesis, with :

$\textcolor{g r e e n}{{\left(k \times {a}^{x}\right)}^{y} = {k}^{y} \times {a}^{x \cdot y}}$

$A = \frac{{\left(- 147\right)}^{4} \cdot \textcolor{g r e e n}{{r}^{36}}}{\textcolor{g r e e n}{{s}^{28}}}$


Therefore :

$A = \frac{466948881 \cdot {r}^{36}}{{s}^{28}}$