Question

find the value of
${125}^{ - 2 \div 3} \times {625}^{5 \div 4 } \div {1 \div 5}^{ - 3}$
​

Answer 1

$\large\underline\blue{\bold{Given \:  Question   }}$

$\pink{ \tt \: :\implies \: {(125)}^{ - \frac{2}{3} } \times {(625)}^{ \frac{5}{4} } \div {( \frac{1}{5} )}^{ - 3} }$

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$\begin{gathered}\Large{\bold{\pink{\underline{Formula \: Used \::}}}} \end{gathered}$

$\begin{gathered}(1)\:{\underline{\boxed{\bf{\blue{a^m\times{a^n}\:=\:a^{m\:+\:n}\:}}}}} \\ \end{gathered}$

$\begin{gathered}(2)\:{\underline{\boxed{\bf{\purple{\dfrac{a^m}{a^n}\:=\:a^{m\:-\:n}\:}}}}} \\ \end{gathered}$

$\begin{gathered}(3)\:{\underline{\boxed{\bf{\orange{\dfrac{1}{x^n}\:=\:x^{-n}\:}}}}} \\ \end{gathered}$

$\begin{gathered}(4)\:{\underline{\boxed{\bf{\color{peru}{(a^m)^n\:=\:a^{m\times{n}}\:}}}}} \\ \end{gathered}$

$\begin{gathered}(5)\:{\underline{\boxed{\bf{\red{ {x}^{0} = 1}}}}} \\ \end{gathered}$

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$\large\underline\purple{\bold{Solution :- }}$

$\tt \: :\implies \: {(125)}^{ - \frac{2}{3} } \times {(625)}^{ \frac{5}{4} } \div {( \frac{1}{5} )}^{ - 3}$

$\tt \: :\implies \: {(5 \times 5 \times 5)}^{ - \frac{2}{3} } \times {(5 \times 5 \times 5 \times 5)}^{ \frac{5}{4} } \times {(5)}^{ - 3}$

$\tt \: :\implies \: {(5)}^{ - \frac{2}{3} \times 3 } \times {(5)}^{ \frac{5}{4} \times 4} \times {(5)}^{ - 3}$

$\tt \: :\implies \: {(5)}^{ - 2} \times {(5)}^{5} \times {(5)}^{ - 3}$

$\tt \: :\implies \: {(5)}^{ - 2 + 5 - 3}$

$\tt \: :\implies \: {(5)}^{0}$

$\tt \: :\implies \: 1$

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