Simplify (x^2y)^3 square root of y^4

${(x^{2} y)}^{3} \sqrt[2]{y^{4}}$

Apply the product rule to $x^{2} y$ .

${(x^{2})}^{3} y^{3} \sqrt{y^{4}}$

Multiply the exponents in ${(x^{2})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{2 \cdot 3} y^{3} \sqrt{y^{4}}$

Multiply $2$ by $3$ .

$x^{6} y^{3} \sqrt{y^{4}}$

Rewrite $y^{4}$ as ${(y^{2})}^{2}$ .

$x^{6} y^{3} \sqrt{{(y^{2})}^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$x^{6} y^{3} y^{2}$

Multiply $y^{3}$ by $y^{2}$ by adding the exponents.

Move $y^{2}$ .

$x^{6} (y^{2} y^{3})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{6} y^{2 + 3}$

Add $2$ and $3$ .

$x^{6} y^{5}$