Algebra Examples

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

Step 1

Move $9^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $9$ as $3^{2}$ .

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

Step 2.2

Multiply the exponents in ${(3^{2})}^{2}$ .

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Step 2.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 2.2.2

Multiply $2$ by $2$ .

$\frac{1}{3^{- 3} \cdot 3^{4}}$

Step 2.3

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

$\frac{1}{3^{- 3 + 4}}$

Step 2.4

Add $- 3$ and $4$ .

$\frac{1}{3^{1}}$

Step 3

Evaluate the exponent.

$\frac{1}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{3}$

Decimal Form:

$0.\overline{3}$