Question

Simplify the radical expression.

Answer 1

`xy^3\sqrt[4]{y^3}`

Explanation:

`\sqrt[4]{x^4y^(15)} =\sqrt[4]{x^4}*\sqrt[4]{y^(15)}\\\\=x\sqrt[4]{y^(15)}\\\\=x(\sqrt[4]{y^(12)} *\sqrt[4]{y^3})\\\\=xy^3\sqrt[4]{y^3}\\\\\\\sqrt[4]{y^(12)} =y^(12/4)=y^3 \\\\\sqrt[4]{x^4} =x^(4/4)=x`

Answer 2

`xy^3 \sqrt[4]{y^3}`

Explanation:

Recall the exponent property
`a^b+a^c=a^((b+c))`.

We can use this property to break the problem down:

`\sqrt[4]{x^4y^(15)}=\sqrt[4]{x\cdot x\cdot x\cdot x\cdot y^3\cdot y^3\cdot y^3\cdot y^3\cdot y^3}=\boxed{xy^3 \sqrt[4]{y^3}}`