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

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

Step 1

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

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

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

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

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

Step 2

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

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

Step 3

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

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

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

Multiply $2$ by $4$ .

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

Step 4

Multiply the exponents in ${(y^{3})}^{4}$ .

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

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

Multiply $3$ by $4$ .

$16 x^{8} y^{12} {(- x y^{2})}^{2}$

Step 5

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

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

$16 x^{8} y^{12} ({(- x)}^{2} {(y^{2})}^{2})$

Apply the product rule to $- x$ .

$16 x^{8} y^{12} ({(- 1)}^{2} x^{2} {(y^{2})}^{2})$

Step 6

Multiply $x^{8}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$16 (x^{2} x^{8}) y^{12} ({(- 1)}^{2} {(y^{2})}^{2})$

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

$16 x^{2 + 8} y^{12} ({(- 1)}^{2} {(y^{2})}^{2})$

Add $2$ and $8$ .

$16 x^{10} y^{12} ({(- 1)}^{2} {(y^{2})}^{2})$

Step 7

Raise $- 1$ to the power of $2$ .

$16 x^{10} y^{12} (1 {(y^{2})}^{2})$

Step 8

Multiply ${(y^{2})}^{2}$ by $1$ .

$16 x^{10} y^{12} {(y^{2})}^{2}$

Step 9

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

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

$16 x^{10} y^{12} y^{2 \cdot 2}$

Multiply $2$ by $2$ .

$16 x^{10} y^{12} y^{4}$

Step 10

Multiply $y^{12}$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

$16 x^{10} (y^{4} y^{12})$

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

$16 x^{10} y^{4 + 12}$

Add $4$ and $12$ .

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

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

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