Algebra Examples

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

Step 1

Simplify the expression.

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Step 1.1

Move $3^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Step 1.2

Move $6^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Step 1.3

Raise $6$ to the power of $2$ .

$\frac{- 1 \cdot 36}{3^{3}}$

Step 1.4

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

$\frac{- 1 \cdot 36}{27}$

Step 1.5

Multiply $- 1$ by $36$ .

$\frac{- 36}{27}$

Step 2

Cancel the common factor of $- 36$ and $27$ .

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Step 2.1

Factor $9$ out of $- 36$ .

$\frac{9 (- 4)}{27}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $9$ out of $27$ .

$\frac{9 \cdot - 4}{9 \cdot 3}$

Step 2.2.2

Cancel the common factor.

$\frac{9 \cdot - 4}{9 \cdot 3}$

Step 2.2.3

Rewrite the expression.

$\frac{- 4}{3}$

Step 3

Move the negative in front of the fraction.

$- \frac{4}{3}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{4}{3}$

Decimal Form:

$- 1.\overline{3}$

Mixed Number Form:

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