Question

Simplify the square root of four over the cubed root of four.

Answer 1

2 will be the answer

Explanation:

Answer 2

`\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}} \\\\\\ ~\hspace{7em}\textit{negative exponents} \\\\ a^(-n) \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^(-n)} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^(-m)\implies a^(n-m) \\\\[-0.35em] \rule{34em}{0.25pt}`

`\bf \cfrac{√(4)}{\sqrt[3]{4}}\implies \cfrac{\sqrt[2]{4}}{\sqrt[3]{4}}\implies \cfrac{4^{(1)/(2)}}{4^{(1)/(3)}}\implies 4^{(1)/(2)}\cdot 4^{-(1)/(3)}\implies 4^{(1)/(2)-(1)/(3)}\implies 4^{(3-2)/(6)} \\\\\\ 4^{(1)/(6)}\implies (2^2)^{(1)/(6)}\implies 2^{2\cdot (1)/(6)}\implies 2(1)/(3)\implies \sqrt[3]{2}`