Question

Which expression is equivalent to (125^2/125^4/3)​

Answer 1

$\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{125^2}{125^{\frac{4}{3}}}\implies \cfrac{(5^3)^2}{(5^3)^{\frac{4}{3}}}\implies \cfrac{5^{3\cdot 2}}{5^{3\cdot \frac{4}{3}}}\implies \cfrac{5^6}{5^4}\\\\\\ 5^6\cdot 5^{-4}\implies 5^{6-4}\implies 5^2\implies 25$