Algebra Examples

$81 \cdot {(\frac{9}{2})}^{- 2}$

Step 1

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

$81 \cdot {(\frac{2}{9})}^{2}$

Step 2

Simplify the expression.

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Step 2.1

Apply the product rule to $\frac{2}{9}$ .

$81 \cdot \frac{2^{2}}{9^{2}}$

Step 2.2

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

$81 \cdot \frac{4}{9^{2}}$

Step 2.3

Raise $9$ to the power of $2$ .

$81 \cdot \frac{4}{81}$

Step 3

Cancel the common factor of $81$ .

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Step 3.1

Cancel the common factor.

$81 \cdot \frac{4}{81}$

Step 3.2

Rewrite the expression.

$4$