[tex]\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\
-----------------------------\\\\
(32x)^{\frac{3}{4}}\qquad 32=2^5\implies (2^5x)^{\frac{3}{4}}\implies \sqrt[4]{(2^5x)^3}\implies \sqrt[4]{2^{5\cdot 3}x^{1\cdot 3}}
\\\\\\
\sqrt[4]{2^{15}x^3}\implies \sqrt[4]{2^{12+3}x^3}\implies \sqrt[4]{2^{12}2^3x^3}\implies \sqrt[4]{(2^3)^42^3x^3}
\\\\\\
2^3\sqrt[4]{2^3x^3}\implies 8\sqrt[4]{8x^3}[/tex]
