Precalculus Examples

$\frac{- 3^{3} \cdot 81^{- 1}}{9^{2}}$

Step 1

Move $81^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 3^{3}}{9^{2} \cdot 81}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{- 3^{3}}{{(3^{2})}^{2} \cdot 81}$

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, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{- 3^{3}}{3^{2 \cdot 2} \cdot 81}$

Step 2.2.2

Multiply $2$ by $2$ .

$\frac{- 3^{3}}{3^{4} \cdot 81}$

Step 2.3

Rewrite $81$ as $3^{4}$ .

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

Step 2.4

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

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

Step 2.5

Add $4$ and $4$ .

$\frac{- 3^{3}}{3^{8}}$

Step 3

Cancel the common factor of $3^{3}$ and $3^{8}$ .

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Step 3.1

Factor $3^{3}$ out of $- 3^{3}$ .

$\frac{3^{3} \cdot - 1}{3^{8}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3^{3}$ out of $3^{8}$ .

$\frac{3^{3} \cdot - 1}{3^{3} \cdot 3^{5}}$

Step 3.2.2

Cancel the common factor.

$\frac{3^{3} \cdot - 1}{3^{3} \cdot 3^{5}}$

Step 3.2.3

Rewrite the expression.

$\frac{- 1}{3^{5}}$

Step 4

Simplify the expression.

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Step 4.1

Raise $3$ to the power of $5$ .

$\frac{- 1}{243}$

Step 4.2

Move the negative in front of the fraction.

$- \frac{1}{243}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{243}$

Decimal Form:

$- 0.00411522 \dots$