Please anyone provide the solution for this problem fast

1.	Please anyone provide the solution for this problem fast
Answer» $\large\underline{\sf{<klux>GIVEN</klux> \:Question - }}$ If $\sf \: \dfrac{ {25}^{n} \times {5}^{3} \times {(125)}^{3} }{5 \times {(625)}^{4} } = 125, \: find \: n.$ $\begin{gathered}\large{\sf{{\underline{Formula \: Used - }}}} \end{gathered}$ $\boxed{ \bf{ \: {x}^{m} \times {x}^{n} = {x}^{m + n}}}$ $\boxed{ \bf{ \: {x}^{m} \div {x}^{n} = {x}^{m - n}}}$ $\boxed{ \bf{ \: {( {x}^{m} )}^{n} = {x}^{mn}}}$ $\boxed{ \bf{ \: {x}^{m} = {x}^{n}\bf\implies \:m = n}}$ $\red{\large\underline{\sf{Solution-}}}$ Given EXPRESSION is $\rm :\longmapsto\:\dfrac{ {25}^{n} \times {5}^{3} \times {(125)}^{3} }{5 \times {(625)}^{4} } = 125$ can be REWRITTEN as $\rm :\longmapsto\:\dfrac{ {(5 \times 5)}^{n} \times {5}^{3} \times {(5 \times 5 \times 5)}^{3} }{5 \times {(5 \times 5 \times 5 \times 5)}^{4} } = 5 \times 5 \times 5$ $\rm :\longmapsto\:\dfrac{ {( {5}^{2} )}^{n} \times {5}^{3} \times {( {5}^{3} )}^{3} }{5 \times {( {5}^{4}) }^{4} } = {5}^{3}$ $\rm :\longmapsto\:\dfrac{ {5}^{2n} \times {5}^{3} \times {5}^{9} }{5 \times {5}^{16} } = {5}^{3}$ $\rm :\longmapsto\:\dfrac{ {5}^{2n + 3 + 9} }{ {5}^{1 + 16} } = {5}^{3}$ $\rm :\longmapsto\:\dfrac{ {5}^{2n + 12} }{ {5}^{17} } = {5}^{3}$ $\rm :\longmapsto\: {5}^{2n + 12 - 17} = {5}^{3}$ $\rm :\longmapsto\: {5}^{2n - 5} = {5}^{3}$ $\rm :\longmapsto\:2n - 5 = 3$ $\rm :\longmapsto\:2n = 3 + 5$ $\rm :\longmapsto\:2n = 8$ $\bf\implies \:n \: = \: 4$ HENCE, For the expression, $\bf :\longmapsto\:\dfrac{ {25}^{n} \times {5}^{3} \times {(125)}^{3} }{5 \times {(625)}^{4} } = 125, \: value \: of\: n \: = \: 4$

Answer»

$\large\underline{\sf{<klux>GIVEN</klux> \:Question - }}$

$\sf \: \dfrac{ {25}^{n} \times {5}^{3} \times {(125)}^{3} }{5 \times {(625)}^{4} } = 125, \: find \: n.$

$\begin{gathered}\large{\sf{{\underline{Formula \: Used - }}}} \end{gathered}$

$\boxed{ \bf{ \: {x}^{m} \times {x}^{n} = {x}^{m + n}}}$

$\boxed{ \bf{ \: {x}^{m} \div {x}^{n} = {x}^{m - n}}}$

$\boxed{ \bf{ \: {( {x}^{m} )}^{n} = {x}^{mn}}}$

$\boxed{ \bf{ \: {x}^{m} = {x}^{n}\bf\implies \:m = n}}$

$\red{\large\underline{\sf{Solution-}}}$

Given EXPRESSION is

$\rm :\longmapsto\:\dfrac{ {25}^{n} \times {5}^{3} \times {(125)}^{3} }{5 \times {(625)}^{4} } = 125$

can be REWRITTEN as

$\rm :\longmapsto\:\dfrac{ {(5 \times 5)}^{n} \times {5}^{3} \times {(5 \times 5 \times 5)}^{3} }{5 \times {(5 \times 5 \times 5 \times 5)}^{4} } = 5 \times 5 \times 5$