How do you simplify $\sqrt[8]{{(a^{16})}^{- 5}}$ $root8((a^16)^-5)$ ?

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Answer 1 · 2016-07-06T21:08:25

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

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

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

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

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

Find a root by dividing the index by the root

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

How do you simplify root8((a^16)^-5)8√(a16)−5root8((a^16)^-5)?