Question

Simplify the radical expression.

Answer 1

Answer:

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

Step-by-step 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

Answer:

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

Step-by-step explanation:

Recall the exponent property $a^b+a^c=a^{(b+c)}$.

We can use this property to break the problem down:

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