Simplify (xy)^5(x^2y)^4

${(x y)}^{5} {(x^{2} y)}^{4}$

Apply the product rule to $x y$ .

$x^{5} y^{5} {(x^{2} y)}^{4}$

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

$x^{5} y^{5} ({(x^{2})}^{4} y^{4})$

Multiply $y^{5}$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

$x^{5} (y^{4} y^{5}) {(x^{2})}^{4}$

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

$x^{5} y^{4 + 5} {(x^{2})}^{4}$

Add $4$ and $5$ .

$x^{5} y^{9} {(x^{2})}^{4}$

Multiply the exponents in ${(x^{2})}^{4}$ .

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

$x^{5} y^{9} x^{2 \cdot 4}$

Multiply $2$ by $4$ .

$x^{5} y^{9} x^{8}$

Multiply $x^{5}$ by $x^{8}$ by adding the exponents.

Move $x^{8}$ .

$x^{8} x^{5} y^{9}$

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

$x^{8 + 5} y^{9}$

Add $8$ and $5$ .

$x^{13} y^{9}$