Algebra Examples

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

Step 1

Apply the product rule to $\frac{2}{3}$ .

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

Step 2

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

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

Step 3

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

$2 (\frac{4}{9}) {(- \frac{1}{2})}^{3}$

Step 4

Multiply $2 (\frac{4}{9})$ .

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Step 4.1

Combine $2$ and $\frac{4}{9}$ .

$\frac{2 \cdot 4}{9} {(- \frac{1}{2})}^{3}$

Step 4.2

Multiply $2$ by $4$ .

$\frac{8}{9} {(- \frac{1}{2})}^{3}$

$\frac{8}{9} {(- \frac{1}{2})}^{3}$

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 5.1

Apply the product rule to $- \frac{1}{2}$ .

$\frac{8}{9} ({(- 1)}^{3} {(\frac{1}{2})}^{3})$

Step 5.2

Apply the product rule to $\frac{1}{2}$ .

$\frac{8}{9} ({(- 1)}^{3} \frac{1^{3}}{2^{3}})$

$\frac{8}{9} ({(- 1)}^{3} \frac{1^{3}}{2^{3}})$

Step 6

Simplify the expression.

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Step 6.1

Raise $- 1$ to the power of $3$ .

$\frac{8}{9} (- \frac{1^{3}}{2^{3}})$

Step 6.2

One to any power is one.

$\frac{8}{9} (- \frac{1}{2^{3}})$

Step 6.3

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

$\frac{8}{9} (- \frac{1}{8})$

$\frac{8}{9} (- \frac{1}{8})$

Step 7

Cancel the common factor of $8$ .

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Step 7.1

Move the leading negative in $- \frac{1}{8}$ into the numerator.

$\frac{8}{9} \cdot \frac{- 1}{8}$

Step 7.2

Cancel the common factor.

$\frac{8}{9} \cdot \frac{- 1}{8}$

Step 7.3

Rewrite the expression.

$\frac{1}{9} \cdot - 1$

$\frac{1}{9} \cdot - 1$

Step 8

Combine $\frac{1}{9}$ and $- 1$ .

$\frac{- 1}{9}$

Step 9

Move the negative in front of the fraction.

$- \frac{1}{9}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{9}$

Decimal Form:

$- 0.\overline{1}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$