Simplify (-2xy^2)^4(2x^3y^4)^2

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

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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

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

Apply the product rule to $- 2 x$ .

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

Raise $- 2$ to the power of $4$ .

$16 x^{4} {(y^{2})}^{4} {(2 x^{3} y^{4})}^{2}$

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

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

$16 x^{4} y^{2 \cdot 4} {(2 x^{3} y^{4})}^{2}$

Multiply $2$ by $4$ .

$16 x^{4} y^{8} {(2 x^{3} y^{4})}^{2}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $2 x^{3} y^{4}$ .

$16 x^{4} y^{8} ({(2 x^{3})}^{2} {(y^{4})}^{2})$

Apply the product rule to $2 x^{3}$ .

$16 x^{4} y^{8} (2^{2} {(x^{3})}^{2} {(y^{4})}^{2})$

Raise $2$ to the power of $2$ .

$16 x^{4} y^{8} (4 {(x^{3})}^{2} {(y^{4})}^{2})$

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

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

$16 x^{4} y^{8} (4 x^{3 \cdot 2} {(y^{4})}^{2})$

Multiply $3$ by $2$ .

$16 x^{4} y^{8} (4 x^{6} {(y^{4})}^{2})$

Multiply $x^{4}$ by $x^{6}$ by adding the exponents.

Move $x^{6}$ .

$16 (x^{6} x^{4}) y^{8} (4 {(y^{4})}^{2})$

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

$16 x^{6 + 4} y^{8} (4 {(y^{4})}^{2})$

Add $6$ and $4$ .

$16 x^{10} y^{8} (4 {(y^{4})}^{2})$

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

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

$16 x^{10} y^{8} (4 y^{4 \cdot 2})$

Multiply $4$ by $2$ .

$16 x^{10} y^{8} (4 y^{8})$

Multiply $y^{8}$ by $y^{8}$ by adding the exponents.

Move $y^{8}$ .

$16 x^{10} (y^{8} y^{8}) \cdot 4$

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

$16 x^{10} y^{8 + 8} \cdot 4$

Add $8$ and $8$ .

$16 x^{10} y^{16} \cdot 4$

Multiply $4$ by $16$ .

$64 x^{10} y^{16}$

Simplify (-2xy^2)^4(2x^3y^4)^2

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