Simplify (-xy)^2(2x^9y^5)^4

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

Step 1

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

Apply the product rule to $- x y$ .

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

Apply the product rule to $- x$ .

${(- 1)}^{2} x^{2} y^{2} {(2 x^{9} y^{5})}^{4}$

Step 2

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

$1 x^{2} y^{2} {(2 x^{9} y^{5})}^{4}$

Step 3

Multiply $x^{2}$ by $1$ .

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

Step 4

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

Apply the product rule to $2 x^{9} y^{5}$ .

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

Apply the product rule to $2 x^{9}$ .

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

Step 5

Rewrite using the commutative property of multiplication.

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

Step 6

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

$16 x^{2} y^{2} ({(x^{9})}^{4} {(y^{5})}^{4})$

Step 7

Multiply the exponents in ${(x^{9})}^{4}$ .

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

$16 x^{2} y^{2} (x^{9 \cdot 4} {(y^{5})}^{4})$

Multiply $9$ by $4$ .

$16 x^{2} y^{2} (x^{36} {(y^{5})}^{4})$

Step 8

Multiply $x^{2}$ by $x^{36}$ by adding the exponents.

Move $x^{36}$ .

$16 (x^{36} x^{2}) y^{2} {(y^{5})}^{4}$

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

$16 x^{36 + 2} y^{2} {(y^{5})}^{4}$

Add $36$ and $2$ .

$16 x^{38} y^{2} {(y^{5})}^{4}$

Step 9

Multiply the exponents in ${(y^{5})}^{4}$ .

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

$16 x^{38} y^{2} y^{5 \cdot 4}$

Multiply $5$ by $4$ .

$16 x^{38} y^{2} y^{20}$

Step 10

Multiply $y^{2}$ by $y^{20}$ by adding the exponents.

Move $y^{20}$ .

$16 x^{38} (y^{20} y^{2})$

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

$16 x^{38} y^{20 + 2}$

Add $20$ and $2$ .

$16 x^{38} y^{22}$

Simplify (-xy)^2(2x^9y^5)^4

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