Question

Which expression is equivalent to 7 sqrt x^2/5 sqrt y^3

Answer 1

The correct option is 1

Explanation:

Given the expression

`\frac{\sqrt[7]{x^2}}{\sqrt[5]{y^3}}`

we have to simplify the above

`\sqrt[7]{x^2}=(x^2)^{(1)/(7)}=x^{(2)/(7)}`

`\sqrt[5]{y^3}=(y^3)^{(1)/(5)}=y^{(3)/(5)}`

The expression becomes

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

Hence, the correct option is 1

Answer 2

Option A
`x^{(2)/(7)}*y^{-(3)/(5)}`

Explanation:

we have

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

we know that

`\sqrt[7]{x^(2)}=x^{(2)/(7)}`

`\sqrt[5]{y^(3)}=y^{(3)/(5)}`

substitute in the expression

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