# How do you simplify root8((a^16)^-5)?

Jul 6, 2016

$\frac{1}{a} ^ 10$

#### Explanation:

Let's start under the root and remove the bracket by multiplying the indices (power to a power law)

$\sqrt[8]{{a}^{-} 80}$

A negative index can be made positive by taking the reciprocal.

Now we have: $\frac{1}{\sqrt[8]{{a}^{80}}}$

Find a root by dividing the index by the root

$\frac{1}{a} ^ 10$