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^{( n)/( m)} \implies \sqrt[ m]{a^ n} ~\hspace{10em} a^{-( n)/( m)} \implies \cfrac{1}{a^{( n)/( m)}} \implies \cfrac{1}{\sqrt[ m]{a^ n}} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{2^{(3)/(4)}}{2^{(1)/(2)}}\implies 2^{(3)/(4)}\cdot 2^{-(1)/(2)}\implies 2^{(3)/(4)-(1)/(2)}\implies 2^{(3-2)/(4)}\implies 2^{(1)/(4)}\implies \sqrt[4]{2^1}\implies \sqrt[4]{2}`