Algebra Examples

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

Step 1

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

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Step 1.1

Move $x^{9}$ .

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

Step 1.2

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

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

Step 1.3

Add $9$ and $5$ .

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

Step 2

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

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Step 2.1

Move $y^{2}$ .

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

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

Step 2.3

Add $2$ and $1$ .

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

Step 3

Multiply $- 4$ by $- 3$ .

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