Question

Rational exponents: quotient rule u^2/5 / u^1/2

Answer 1

$\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{u^{\frac{2}{5}}}{r^{\frac{1}{2}}}\implies \cfrac{1}{u^{\frac{1}{2}}\cdot u^{-\frac{2}{5}}}\implies \cfrac{1}{u^{\frac{1}{2}-\frac{2}{5}}}\implies \cfrac{1}{u^{\frac{5-4}{10}}}\implies \cfrac{1}{u^{\frac{1}{10}}}\implies u^{-\frac{1}{10}}$