# How do you write 32^(-3/5) in radical form?

##### 2 Answers
Jun 4, 2018

Se explanation below

#### Explanation:

We define ${a}^{\frac{m}{n}} = \sqrt[n]{{a}^{m}}$.

By other hand, we know that ${a}^{- n} = \frac{1}{a} ^ n$

With these rules in mind, in our case

32^(-3/5)=1/(root(5)(32^3))=1/(root(5)((2^5)^3))=1/(root(5)(2^15))=1/root(5)(2^5·2^5·2^5)=1/8

Jun 4, 2018

$\frac{1}{8}$

#### Explanation:

${32}^{- \frac{3}{5}}$

$\therefore = {\left({2}^{5}\right)}^{- \frac{3}{5}}$

$\therefore = {2}^{- \frac{15}{5}}$

$\therefore = {2}^{-} 3$

$\therefore = {m}^{-} 3 = \frac{1}{m} ^ 3$

$\therefore = \frac{1}{2} ^ 3$

$\therefore = \frac{1}{8}$