Evaluate |(1/2)÷(1/4)|^8

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

To divide by a fraction, multiply by its reciprocal.

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

Cancel the common factor of $2$ .

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Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

${| 2 |}^{8}$

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

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Factor $2$ out of $4$ .

${(\frac{1}{2} \cdot (2 (2)))}^{8}$

Cancel the common factor.

${(\frac{1}{2} \cdot (2 \cdot 2))}^{8}$

Rewrite the expression.

$2^{8}$

Raise $2$ to the power of $8$ .

$256$

Evaluate |(1/2)÷(1/4)|^8

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