Question

express ³√x^7 y^5 in index form​

Answer 1

$Given \: \sqrt[3] { x^{7} y^{5} }$

$= \Big( x^{7} y^{5} \Big)^{\frac{1}{3} }$

$= \Big( x^{7}\Big)^{\frac{1}{3}} \times \Big( y^{5} \Big)^{\frac{1}{3}}$

$= x^{\frac{7}{3}} y^{\frac{5}{3}}$

/* By Exponential Law */

$\boxed{ \pink{ (ab)^{n} = a^{n} \times b^{n} }}$

Therefore.,

$\red{Index \:form \:of \:\sqrt[3] { x^{7} y^{5} }}$

$\green {= x^{\frac{7}{3}} y^{\frac{5}{3}} }$

•••♪

Answer 2

$\huge \underline{answer} \\ \sf \implies \: \sqrt[3]{ {x}^{7} {y}^{5} } \\ \\ \sf \implies \: ( {x}^{7} {y}^{5} ) ^{ \frac{1}{3} } \\ \\ \sf \implies \: ({x}^{7} ) ^{ \frac{1}{3} } ( {y}^{5} ) ^{ \frac{1}{3} } \\ \\ \sf \implies \:( {x}^{ \frac{7}{3} } )( {y}^{ \frac{5}{3} } )$