Simplify x^2(xy^3)^2+y^2(x^2y^2)^2

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

Simplify each term.

Apply the product rule to $x y^{3}$ .

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

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

Move $x^{2}$ .

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

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

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

Add $2$ and $2$ .

$x^{4} {(y^{3})}^{2} + y^{2} {(x^{2} y^{2})}^{2}$

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

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

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

Multiply $3$ by $2$ .

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

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

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

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

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

$x^{4} y^{6} + y^{2} (x^{2 \cdot 2} {(y^{2})}^{2})$

Multiply $2$ by $2$ .

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

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

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

$x^{4} y^{6} + y^{2} (x^{4} y^{2 \cdot 2})$

Multiply $2$ by $2$ .

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

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

Move $y^{4}$ .

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

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

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

Add $4$ and $2$ .

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

Add $x^{4} y^{6}$ and $y^{6} x^{4}$ .

Reorder $y^{6}$ and $x^{4}$ .

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

Add $x^{4} y^{6}$ and $x^{4} y^{6}$ .

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