Question

Which expression is equivalent to ? Assume .

Answer 1

`\text{Use}\ \sqrt[n]{a^m}=a^{(m)/(n)}\ \text{and}\ a^(-1)=\dfac{1}{a}\\\\\frac{\sqrt[7]{x^2}}{\sqrt[5]{y^3}}=\left(x^{(2)/(7)\right)\left((1)/(y^(3)/(5))\right)=\left(x^{(2)/(7)}\right)\left(y^{-(3)/(5)}\right)`

Answer 2

Answer:
`(x^{(2)/(7)})(y^{-(3)/(5)})`

Explanation:

The given expression :
`\frac{\sqrt[7]{x^2}}{\sqrt[5]{y^3} }`

Law of radicals :-

`\sqrt[n]{a}=a^{(1)/(n)}\\\\\sqrt[n]{a^m}=a^{(m)/(n)}`

Law of exponent:

`(1)/(a^n)=a^(-n)`

Using the above law of radicals and law of exponent we have,

`\frac{\sqrt[7]{x^2}}{\sqrt[5]{y^3}}\\\\=(x^{(2)/(7)})(y^{-(3)/(5)})`