Question

9^-3/9^6 using single positive exponent

Answer 1

`~\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] ~\dotfill\\\\ \cfrac{9^(-3)}{9^6}\implies \cfrac{9^(-3)}{1}\cdot \cfrac{1}{9^6}\implies \cfrac{1}{9^3}\cdot \cfrac{1}{9^6}\implies \cfrac{1}{9^3 9^6}\implies \cfrac{1}{9^(3+6)}\implies \cfrac{1}{9^(9)}`