Pre-Algebra Examples

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

Step 1

Rewrite using the commutative property of multiplication.

$- \frac{1}{2} \cdot \frac{2}{3} x^{2} x$

Step 2

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

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Step 2.1

Move $x$ .

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

Step 2.2

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

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Step 2.2.1

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

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

Step 2.2.2

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

$- \frac{1}{2} \cdot \frac{2}{3} x^{1 + 2}$

Step 2.3

Add $1$ and $2$ .

$- \frac{1}{2} \cdot \frac{2}{3} x^{3}$

Step 3

Cancel the common factor of $2$ .

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Step 3.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$\frac{- 1}{2} \cdot \frac{2}{3} x^{3}$

Step 3.2

Cancel the common factor.

$\frac{- 1}{2} \cdot \frac{2}{3} x^{3}$

Step 3.3

Rewrite the expression.

$- 1 \cdot \frac{1}{3} x^{3}$

Step 4

Rewrite $- 1 (\frac{1}{3})$ as $- (\frac{1}{3})$ .

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

Step 5

Combine $x^{3}$ and $\frac{1}{3}$ .

$- \frac{x^{3}}{3}$