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

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

Step 1

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

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

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

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

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

Step 2

Raise $2$ to the power of $3$ .

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

Step 3

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

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

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

Multiply $3$ by $3$ .

$8 x^{9} {(y^{3})}^{3} \cdot {(- x^{2} y)}^{4}$

Step 4

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

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

$8 x^{9} y^{3 \cdot 3} \cdot {(- x^{2} y)}^{4}$

Multiply $3$ by $3$ .

$8 x^{9} y^{9} \cdot {(- x^{2} y)}^{4}$

Step 5

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

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

$8 x^{9} y^{9} \cdot ({(- x^{2})}^{4} y^{4})$

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

$8 x^{9} y^{9} \cdot ({(- 1)}^{4} {(x^{2})}^{4} y^{4})$

Step 6

Multiply $y^{9}$ by $y^{4}$ by adding the exponents.

Move $y^{4}$ .

$8 x^{9} (y^{4} y^{9}) \cdot ({(- 1)}^{4} {(x^{2})}^{4})$

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

$8 x^{9} y^{4 + 9} \cdot ({(- 1)}^{4} {(x^{2})}^{4})$

Add $4$ and $9$ .

$8 x^{9} y^{13} \cdot ({(- 1)}^{4} {(x^{2})}^{4})$

Step 7

Raise $- 1$ to the power of $4$ .

$8 x^{9} y^{13} \cdot (1 {(x^{2})}^{4})$

Step 8

Multiply ${(x^{2})}^{4}$ by $1$ .

$8 x^{9} y^{13} \cdot {(x^{2})}^{4}$

Step 9

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

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

$8 x^{9} y^{13} \cdot x^{2 \cdot 4}$

Multiply $2$ by $4$ .

$8 x^{9} y^{13} \cdot x^{8}$

Step 10

Multiply $x^{9}$ by $x^{8}$ by adding the exponents.

Move $x^{8}$ .

$8 (x^{8} x^{9}) y^{13}$

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

$8 x^{8 + 9} y^{13}$

Add $8$ and $9$ .

$8 x^{17} y^{13}$

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

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