Algebra Examples

$\frac{1}{6} {(\frac{2}{3})}^{- 2}$

Step 1

Change the sign of the exponent by rewriting the base as its reciprocal.

$\frac{1}{6} \cdot {(\frac{3}{2})}^{2}$

Step 2

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

$\frac{1}{6} \cdot \frac{3^{2}}{2^{2}}$

Step 3

Combine.

$\frac{1 \cdot 3^{2}}{6 \cdot 2^{2}}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $3^{2}$ by $1$ .

$\frac{3^{2}}{6 \cdot 2^{2}}$

Step 4.2

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

$\frac{3^{2}}{6 \cdot 4}$

Step 4.3

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

$\frac{9}{6 \cdot 4}$

Step 4.4

Multiply $6$ by $4$ .

$\frac{9}{24}$

$\frac{9}{24}$

Step 5

Cancel the common factor of $9$ and $24$ .

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Step 5.1

Factor $3$ out of $9$ .

$\frac{3 (3)}{24}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Factor $3$ out of $24$ .

$\frac{3 \cdot 3}{3 \cdot 8}$

Step 5.2.2

Cancel the common factor.

$\frac{3 \cdot 3}{3 \cdot 8}$

Step 5.2.3

Rewrite the expression.

$\frac{3}{8}$

$\frac{3}{8}$

$\frac{3}{8}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{3}{8}$

Decimal Form:

$0.375$

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