# How do you simplify (-243)^(3/5)?

-27

#### Explanation:

With this type of question, see that an exponent in the form of $\frac{a}{b}$ means that we should take the base number to the $a$ power and also take the $b$th root.

In our case, we're being asked to take -243 to the 3rd power and also to take the 5th root. This will be easier if we first see that:

$- 243 = {\left(- 3\right)}^{5}$

And so we can rewrite our question as

${\left(- 243\right)}^{\frac{3}{5}} = {\left({\left(- 3\right)}^{5}\right)}^{\frac{3}{5}}$

We can now apply the rule that

${\left({x}^{a}\right)}^{b} = {x}^{a b}$

${\left({\left(- 3\right)}^{5}\right)}^{\frac{3}{5}} = {\left(- 3\right)}^{5 \times \left(\frac{3}{5}\right)} = {\left(- 3\right)}^{3} = - 27$