Find the Product (-3x^5y)(-4x^9y^2)

$(- 3 x^{5} y) (- 4 x^{9} y^{2})$

Step 1

Multiply $x^{5}$ by $x^{9}$ by adding the exponents.

Move $x^{9}$ .

$- 3 (x^{9} x^{5}) y (- 4 y^{2})$

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

$- 3 x^{9 + 5} y (- 4 y^{2})$

Add $9$ and $5$ .

$- 3 x^{14} y (- 4 y^{2})$

Step 2

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

Move $y^{2}$ .

$- 3 x^{14} (y^{2} y) \cdot - 4$

Multiply $y^{2}$ by $y$ .

Raise $y$ to the power of $1$ .

$- 3 x^{14} (y^{2} y^{1}) \cdot - 4$

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

$- 3 x^{14} y^{2 + 1} \cdot - 4$

Add $2$ and $1$ .

$- 3 x^{14} y^{3} \cdot - 4$

Step 3

Multiply $- 4$ by $- 3$ .

$12 x^{14} y^{3}$