Find the Product (-2^2x^3y^4)((-3)^2x^4y^4)

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

Step 1

Multiply $x^{3}$ by $x^{4}$ by adding the exponents.

Move $x^{4}$ .

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

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

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

Add $4$ and $3$ .

$- 2^{2} x^{7} y^{4} ({(- 3)}^{2} y^{4})$

Step 2

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

Move $y^{4}$ .

$- 2^{2} x^{7} (y^{4} y^{4}) {(- 3)}^{2}$

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

$- 2^{2} x^{7} y^{4 + 4} {(- 3)}^{2}$

Add $4$ and $4$ .

$- 2^{2} x^{7} y^{8} {(- 3)}^{2}$

Step 3

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

$- 1 \cdot 4 x^{7} y^{8} {(- 3)}^{2}$

Step 4

Multiply $- 1$ by $4$ .

$- 4 x^{7} y^{8} {(- 3)}^{2}$

Step 5

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

$- 4 x^{7} y^{8} \cdot 9$

Step 6

Multiply $9$ by $- 4$ .

$- 36 x^{7} y^{8}$