# Simplify rootx(a^y)? for example, root8(5^6)

##### 1 Answer
Jun 6, 2017

${5}^{\setminus \frac{3}{4}}$

#### Explanation:

$\sqrt[x]{a}$ can also be represented as ${a}^{\setminus \frac{1}{x}}$, for instance $\sqrt{4} = {4}^{\frac{1}{2}}$. Therefore $\sqrt[x]{{a}^{y}} = {\left({a}^{y}\right)}^{\setminus \frac{1}{x}}$, and with indices laws we can simplify that to ${a}^{y \cdot \setminus \frac{1}{x}} = {a}^{\setminus \frac{y}{x}}$.
In the case of $\sqrt[8]{{5}^{6}} = {5}^{\setminus \frac{6}{8}}$, which simplifies to ${5}^{\setminus \frac{3}{4}}$, which you could write as $\sqrt[4]{{5}^{3}}$.
Apart from that however you can't simplify whilst keeping it in exact form.