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

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

Step 1

Apply the product rule to $x y$ .

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

Step 2

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

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

Step 3

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

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

$x^{2} y^{2} (x^{2 \cdot 2} {(y^{2})}^{2})$

Multiply $2$ by $2$ .

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

Step 4

Multiply $x^{2}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

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

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

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

Add $4$ and $2$ .

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

Step 5

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

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

$x^{6} y^{2} y^{2 \cdot 2}$

Multiply $2$ by $2$ .

$x^{6} y^{2} y^{4}$

Step 6

Multiply $y^{2}$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

$x^{6} (y^{4} y^{2})$

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

$x^{6} y^{4 + 2}$

Add $4$ and $2$ .

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