[tex]\bf a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n}
\qquad \qquad
\sqrt[ m]{a^ n}\implies a^{\frac{ n}{ m}}\\\\
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\left( \cfrac{16y^5}{4y^3} \right)^{\frac{1}{2}}\implies \left( \cfrac{4^2y^5}{2^2y^3} \right)^{\frac{1}{2}}\impliedby \textit{let's distribute the exponent}[/tex]
[tex]\bf \left( \cfrac{4^{2\cdot \frac{1}{2}}y^{5\cdot \frac{1}{2}}}{2^{2\cdot \frac{1}{2}}y^{3\cdot \frac{1}{3}}} \right)\implies \cfrac{4^1y^{\frac{5}{2}}}{2^1y^1}\implies \cfrac{4y^{\frac{5}{2}y^{-1}}}{2}\implies \cfrac{4y^{\frac{5}{2}-1}}{2}\implies \cfrac{4y^{\frac{3}{2}}}{2}
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\cfrac{2y^{\frac{3}{2}}}{1}\implies 2\sqrt[2]{y^3}\implies 2\sqrt{y^{2+1}}\implies 2\sqrt{y^2y}\implies 2y\sqrt{y}[/tex]
