# To write: The radical expression using exponent y^{-frac{5}{3}}

To write:
The radical expression using exponent ${y}^{-\frac{5}{3}}$
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estenutC
Step 1
Definition used:
For any rational exponent $\frac{m}{n}$ in lowest terms, where m and n are integers and $n>0,$ we define
${a}^{\frac{m}{n}}={\left(\sqrt{n}\left\{a\right\}\right)}^{m}$ or equivalently ${a}^{\frac{m}{n}}=\sqrt{n}\left\{{a}^{m}\right\}$
If n is even, then we require that $a\ge 0.$
Step 2
Consider, ${y}^{-\frac{5}{3}}$
From the above definition ${a}^{\frac{m}{n}}={\left(\sqrt{n}\left\{a\right\}\right)}^{m}$ the exponent notation of ${y}^{-\frac{5}{3}}$ is written as,
${y}^{-\frac{5}{3}}=\frac{1}{{y}^{\frac{5}{3}}}$
$=\frac{1}{{\left({y}^{5}\right)}^{\frac{1}{3}}}$
${y}^{-\frac{5}{3}}=\frac{1}{\sqrt{3}\left\{{y}^{5}\right\}}$
Therefore radical notation of the radical ${y}^{-\frac{5}{3}}$ is $\frac{1}{\sqrt{3}\left\{{y}^{5}\right\}}$