# Simplify expression and express your answer using rational indicators. Suppose all letters represent positive numbers: \frac{1}{\sqrt[5]{x^{3}}}ZSK

Simplify expression and express your answer using rational indicators. Suppose all letters represent positive numbers.
$\frac{1}{\sqrt[5]{{x}^{3}}}$

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Step 1
Concept used:
If a - a real number, n - positive integer
$\sqrt[n]{{a}^{m}}={a}^{mn}$
The above statement can be expressed as,
$\frac{1}{{a}^{n}}={a}^{-n}$
Step 2
The property of n the root after combine the $\frac{1}{{a}^{n}}={a}^{-n}$ and $\sqrt[n]{{a}^{m}}={a}^{\frac{m}{n}}$ is,
$\frac{1}{\sqrt[n]{{a}^{m}}}={a}^{-\frac{m}{n}}$
Substitute 5 for n, 3 for m and x for a in the above equation.
$\frac{1}{\sqrt[5]{{x}^{3}}}=\frac{1}{{\left({x}^{\frac{1}{5}}\right)}^{3}}$
$={\left({x}^{\frac{1}{5}}\right)}^{-3}$
$={x}^{-\frac{3}{5}}$
Thus, the solution of the expression $\frac{1}{\sqrt[5]{{x}^{3}}}$ is ${x}^{-\frac{3}{5}}$