# How do you simplify and write (-r^4s)^2 (-r^2s^5)^5 with positive exponents?

Jan 14, 2017

$= - {r}^{18} {s}^{27}$

#### Explanation:

To simplify you need to get rid of the brackets first:

$\textcolor{b l u e}{{\left(- {r}^{4} s\right)}^{2}} \textcolor{red}{{\left(- {r}^{2} {s}^{5}\right)}^{5}}$

Use the law of indices: ${\left({x}^{m}\right)}^{n} = {x}^{m n}$

Note that: an odd number of negative signs gives a negative while an even number gives a positive.

$= \textcolor{b l u e}{+ {r}^{8} {s}^{2}} \times \textcolor{red}{- {r}^{10} {s}^{25}}$

Now to simplify, use the law of indices....

${x}^{m} \times {x}^{n} = {x}^{m + n}$

$= - {r}^{18} {s}^{27}$

Note that the negative sign is not the same as a negative index.