Algebra Examples

$| {(- \frac{1}{2})}^{3} \div {(\frac{1}{4})}^{2} |$

Step 1

Rewrite the division as a fraction.

$| \frac{{(- \frac{1}{2})}^{3}}{{(\frac{1}{4})}^{2}} |$

Step 2

Simplify the numerator.

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Step 2.1

Apply the product rule to $- \frac{1}{2}$ .

$| \frac{{(- 1)}^{3} {(\frac{1}{2})}^{3}}{{(\frac{1}{4})}^{2}} |$

Step 2.2

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

$| \frac{- {(\frac{1}{2})}^{3}}{{(\frac{1}{4})}^{2}} |$

Step 2.3

Apply the product rule to $\frac{1}{2}$ .

$| \frac{- \frac{1^{3}}{2^{3}}}{{(\frac{1}{4})}^{2}} |$

Step 2.4

One to any power is one.

$| \frac{- \frac{1}{2^{3}}}{{(\frac{1}{4})}^{2}} |$

Step 2.5

Raise $2$ to the power of $3$ .

$| \frac{- \frac{1}{8}}{{(\frac{1}{4})}^{2}} |$

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $\frac{1}{4}$ .

$| \frac{- \frac{1}{8}}{\frac{1^{2}}{4^{2}}} |$

Step 3.2

One to any power is one.

$| \frac{- \frac{1}{8}}{\frac{1}{4^{2}}} |$

Step 3.3

Raise $4$ to the power of $2$ .

$| \frac{- \frac{1}{8}}{\frac{1}{16}} |$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$| - \frac{1}{8} \cdot 16 |$

Step 5

Cancel the common factor of $8$ .

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Step 5.1

Move the leading negative in $- \frac{1}{8}$ into the numerator.

$| \frac{- 1}{8} \cdot 16 |$

Step 5.2

Factor $8$ out of $16$ .

$| \frac{- 1}{8} \cdot (8 (2)) |$

Step 5.3

Cancel the common factor.

$| \frac{- 1}{8} \cdot (8 \cdot 2) |$

Step 5.4

Rewrite the expression.

$| - 1 \cdot 2 |$

Step 6

Multiply $- 1$ by $2$ .

$| - 2 |$

Step 7

The absolute value is the distance between a number and zero. The distance between $- 2$ and $0$ is $2$ .

$2$