Question

Which expression is equivalent to 3√32x^8y^10?

Answer 1

Third option is correct.

Explanation:

The given expression is,

`\sqrt[3]{32x^8y^(10)}`

The expression can be written as,

`\sqrt[3]{(2)^5x^8y^(10)}`

Use exponent rule
`x^(m+n)=x^m.x^n`,

`\sqrt[3]{(2)^(3+2)x^(6+2)y^(9+1)}`

`\sqrt[3]{2^3* 2^2* x^6* x^2* y^9* y}`

`\sqrt[3]{2^3* (x^2)^3* (y^3)^3* 2^2* x^2* y}`

`\sqrt[3]{(2x^2y^3)^3* 2^2* x^2* y}`

`2x^2y^3\sqrt[3]{2^2* x^2* y}`

`2x^2y^3\sqrt[3]{4x^2y}`

Therefore the third option is correct.

Answer 2

see attached picture