Question

3-⁵x 10-⁵ x 125
___________
5-⁷ x 6-⁵.


pls answer fast ​

Answer 1

please refer to attachment above

Answer 2

Step by step Explanation

$~~~~~:~~\implies\sf \dfrac { {3}^{ - 5} \times {10}^{ - 5} \times 125}{ {5}^{ - 7} \times {6}^{ - 5} }$

$~~~~~:~~\implies\sf \dfrac { {3}^{ - 5} \times {(2 \times 5)}^{ - 5} \times 125}{ {5}^{ - 7} \times {(2 \times 3)}^{ - 5} }$

$~~~~~:~~\implies\sf \dfrac { \cancel{ {3}^{ - 5}} \times \cancel{ (2)^{ - 5}} \times {5}^{ - 5} \times {5}^{3} }{ {5}^{ - 7} \times \cancel{ {2}^{ - 5}} \times \cancel{{3}^{ - 5}} }$

$~~~~~:~~\implies\sf \dfrac { {5}^{ - 5 + 3} }{ {5}^{ - 7} }$

$~~~~~:~~\implies\sf \dfrac { {5}^{ - 2} }{ {5}^{ - 7} }$

$~~~~~:~~\implies\sf \dfrac { \dfrac{1}{ {5}^{2} } }{ \dfrac{1}{ {5}^{7} } }$

$~~~~~:~~\implies\sf \dfrac{1}{25} \times 78125$

$~~~~~:~~\implies\sf 3125$

$\boxed{ ~~~~~\sf \dfrac { {3}^{ - 5} \times {10}^{ - 5} \times 125}{ {5}^{ - 7} \times {6}^{ - 5} }=\bf 3125 }$

• $\blue{\tiny\begin{gathered}\begin{gathered}\\\\\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered} \bigstar \: \underline{\bf{}}\\ {\boxed{\begin{array}{c | c} \frac{ \: ~~~~~~~~~~\: \: \: \: \:\sf \red{ Laws} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{ } &\frac{ \: ~~~~~~~~~~ \: \: \: \: \:\sf \pink{Example} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }{ }\\ \sf \bigstar{a}^{m} \times {a}^{n} = {a}^{m + n} & \sf {a}^{2} \times {a}^{3} = {a}^{2 + 3} = {a}^{6} \\ \\ \sf \bigstar{a}^{m} \div {a}^{n} = {a}^{m - n}& \sf {a}^{3} \div {a}^{2} = {a}^{3 - 2} = {a}^{1} \\ \\ \sf{\bigstar \: \: \: \: \: \: ( {a}^{m} ) ^{n} = {a}^{mn} } & \sf( {a}^{2} ) ^{3} = {a}^{2 \times 3} = {a}^{6} \\ \\ {\bigstar\sf a {}^{m} \times {n}^{m} = (ab) ^{m} } &\sf a {}^{2} \times {b}^{2} = (ab) ^{2}\\ \\ \sf\bigstar \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: {a}^{0} = 1& \sf {2}^{0} = 1 \: \: \: \: \\ \\ \sf \bigstar \: \: \: \: {\dfrac{ {a}^{m} }{ {b}^{m} }= \left( \dfrac{a}{b} \right) ^{m} }& \sf{\dfrac{ {a}^{2} }{ {b}^{2} }= \left( \dfrac{a}{b} \right) ^{2} }\\\\\bigstar~~~~~~~ \sf x^{\frac{m}{n} }=\sqrt[n]{x^m}\sf = (\sqrt[n]{x})^m & \sf x^{\frac{2}{3} }=\sqrt[3]{x^2} = (\sqrt[n]{x})^m\\ \\\\ \end{array}}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}}$