Question

Which expression is equivalent to ^3√x^5y?
a)x5/3
b)x5/3y1/3
c)x3/5 y
d)x3/5 y3​

Answer 1

`(x^5y)^{(1)/(3)}= x^{(5)/(3)} * y^{(1)/(3)}`

Explanation:

We are given our expression as

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

The property of exponent says that

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

Hence

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

Another property says

`(ab)^n=a^n * b^n`

Hence

`(x^5y)^{(1)/(3)}= x^{(5)/(3)} * y^{(1)/(3)}`

Hence option B is correct.