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^{(2)/(5)}}{r^{(1)/(2)}}\implies \cfrac{1}{u^{(1)/(2)}\cdot u^{-(2)/(5)}}\implies \cfrac{1}{u^{(1)/(2)-(2)/(5)}}\implies \cfrac{1}{u^{(5-4)/(10)}}\implies \cfrac{1}{u^{(1)/(10)}}\implies u^{-(1)/(10)}`