Algebra Examples

$(- 15 x y^{4}) (- \frac{1}{3} x y^{3})$

Step 1

Multiply $x$ by $x$ by adding the exponents.

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Step 1.1

Move $x$ .

$- 15 (x \cdot x) y^{4} (- \frac{1}{3} \cdot (y^{3}))$

Step 1.2

Multiply $x$ by $x$ .

$- 15 x^{2} y^{4} (- \frac{1}{3} \cdot (y^{3}))$

Step 2

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

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Step 2.1

Move $y^{3}$ .

$- 15 x^{2} (y^{3} y^{4}) (- \frac{1}{3})$

Step 2.2

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

$- 15 x^{2} y^{3 + 4} (- \frac{1}{3})$

Step 2.3

Add $3$ and $4$ .

$- 15 x^{2} y^{7} (- \frac{1}{3})$

Step 3

Cancel the common factor of $3$ .

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Step 3.1

Move the leading negative in $- \frac{1}{3}$ into the numerator.

$- 15 x^{2} y^{7} \frac{- 1}{3}$

Step 3.2

Factor $3$ out of $- 15 x^{2} y^{7}$ .

$3 (- 5 x^{2} y^{7}) \frac{- 1}{3}$

Step 3.3

Cancel the common factor.

$3 (- 5 x^{2} y^{7}) \frac{- 1}{3}$

Step 3.4

Rewrite the expression.

$- 5 x^{2} y^{7} \cdot - 1$

Step 4

Multiply $- 1$ by $- 5$ .

$5 x^{2} y^{7}$