Question

What is the value of m in the quotient of powers

Answer 1

$\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \cfrac{9^{-3}}{9^2}=\cfrac{1}{9^m}\implies 9^{-3}\cdot 9^{-2}=1\cdot 9^{-m}\implies 9^{-3-2}=9^{-m}\implies 9^{-5}=9^{-m} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill 5=m~\hfill$