Basic Math Examples

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

Step 1

Move the negative in front of the fraction.

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

Step 2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.1

Apply the product rule to $- \frac{3}{4}$ .

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

Step 2.2

Apply the product rule to $\frac{3}{4}$ .

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

Step 3

Evaluate the exponents.

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Step 3.1

Raise $- 1$ to the power of $3$ .

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

Step 3.2

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

$- \frac{27}{4^{3}} \cdot \frac{1}{3}$

Step 3.3

Raise $4$ to the power of $3$ .

$- \frac{27}{64} \cdot \frac{1}{3}$

Step 4

Cancel the common factor of $3$ .

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Step 4.1

Move the leading negative in $- \frac{27}{64}$ into the numerator.

$\frac{- 27}{64} \cdot \frac{1}{3}$

Step 4.2

Factor $3$ out of $- 27$ .

$\frac{3 (- 9)}{64} \cdot \frac{1}{3}$

Step 4.3

Cancel the common factor.

$\frac{3 \cdot - 9}{64} \cdot \frac{1}{3}$

Step 4.4

Rewrite the expression.

$\frac{- 9}{64}$

Step 5

Move the negative in front of the fraction.

$- \frac{9}{64}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{9}{64}$

Decimal Form:

$- 0.140625$