Question

Which expression is equivalent to 3 sqrt32x8y10?

O 4x2y3(3 sqrt2x2y)
O 2x4y5(3 sqrt4)
O 2x2y3(3 sqrt4x2y)
O 4x4y5(3 sqrt2)​

Answer 1

Option C :

`\sqrt[3]{32x^8y^10} = 2x^2 y^3 \sqrt[3]{4x^2 y}`

Explanation:

`\sqrt[3]{32x^8y^(10)}} = ( 32 x^8 y^(10))^{(1)/(3)}`

`= ( 2^5 * x^8 * y^(10))^{(1)/(3)}\\\\= ( 2^{5*(1)/(3)} * x^{8 * (1)/(3)} * y^{10 * (1)/(3)})\\\\=(2^{(3)/(3) + (2)/(3)}} * x^{(6)/(3) + (2)/(3)} * y^{(9)/(3) + (1)/(3)})\\\\= 2 * 2^{(2)/(3)} x^2 * x^{(2)/(3)} * y^3 * y^(1)/(3)\\\\=2x^2 y^3 * 2^{(2)/(3) * }x^{(2)/(3)} * y^{(1)/(3)}\\\\=2x^2 y^3 (2^2x^2 y)^{(1)/(3)}\\\\= 2x^2y^3 \ \sqrt[3]{ \ 4 x^2 \ y }`

Answer 2

Answer:
`2x^(2) y^(3) (\sqrt[3]{4x^(2) y} )`

Explanation:

`\sqrt[3]{32x^(8) y^(10) } =\sqrt[3]{2^(3) \cdot 2^(2) \cdot x^(2) \cdot (x^(2) )^(3) \cdot y \cdot (y^(3))^(3) } =2x^(2) y^(3) (\sqrt[3]{4x^(2) y} )`