Question

Solve the question , add steps .​

Answer 1

`\boxed{15625}`

`\boxed{\underline{ \rm{Step-by-step \: explanation:-}}}`

`\displaystyle{ \frac{ {5}^(3) }{ {5}^( - 3) } }`

`= \displaystyle{ {5}^(3 - ( - 3)) }`

`= \displaystyle{ {5}^(3 + 3) }`

`= \displaystyle{ {5}^(6) }`

`= (5 * 5 * 5 * 5 * 5 * 5)`

`= \displaystyle{15625}`

Answer 2

`~\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{5^3}{5^(-3)}\implies \cfrac{5^3}{1}\cdot \cfrac{1}{5^(-3)}\implies 5^3\cdot 5^3\implies 5^(3+6)\implies 5^6\implies \text{\LARGE 15625}`