Question

What is equivalent to 10/10^3/4

Answer 1

`\bf ~\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) \\\\\\ ~\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}`

`\bf \cfrac{10}{10^{(3)/(4)}}\implies \cfrac{10^1}{10^{(3)/(4)}}\implies \cfrac{10^{(4)/(4)}}{10^{(3)/(4)}}\implies 10^{(4)/(4)}\cdot 10^{-(3)/(4)}\implies 10^{(4)/(4)-(3)/(4)}\implies 10^{(1)/(4)}\implies \sqrt[4]{10}`