Question

ewrite the rational exponent as a radical by extending the properties of integer exponents. 2 to the 3 over 4 power, all over 2 to the 1 over 2 power

Answer 1

$\bf ~\hspace{7em}\textit{rational exponents} \\\\ a^{\frac{ n}{ m}} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-\frac{ n}{ m}} \implies \cfrac{1}{a^{\frac{ n}{ m}}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{2^{\frac{3}{4}}}{2^{\frac{1}{2}}}\implies 2^{\frac{3}{4}}\cdot 2^{-\frac{1}{2}}\implies 2^{\frac{3}{4}-\frac{1}{2}}\implies 2^{\frac{3-2}{4}}\implies 2^{\frac{1}{4}}\implies \sqrt[4]{2^1}\implies \sqrt[4]{2}$