Algebra Examples

$\frac{3^{- 3} {(- 2)}^{- 5}}{6^{- 1}}$

Step 1

Simplify the expression.

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Step 1.1

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

$\frac{{(- 2)}^{- 5}}{6^{- 1} \cdot 3^{3}}$

Step 1.2

Move ${(- 2)}^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{6^{- 1} \cdot 3^{3} {(- 2)}^{5}}$

Step 1.3

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

$\frac{6}{3^{3} {(- 2)}^{5}}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{6}{27 {(- 2)}^{5}}$

Step 2.2

Raise $- 2$ to the power of $5$ .

$\frac{6}{27 \cdot - 32}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Multiply $27$ by $- 32$ .

$\frac{6}{- 864}$

Step 3.2

Cancel the common factor of $6$ and $- 864$ .

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Step 3.2.1

Factor $6$ out of $6$ .

$\frac{6 (1)}{- 864}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $6$ out of $- 864$ .

$\frac{6 \cdot 1}{6 \cdot - 144}$

Step 3.2.2.2

Cancel the common factor.

$\frac{6 \cdot 1}{6 \cdot - 144}$

Step 3.2.2.3

Rewrite the expression.

$\frac{1}{- 144}$

Step 3.3

Move the negative in front of the fraction.

$- \frac{1}{144}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{144}$

Decimal Form:

$- 0.0069\overline{4}$