Algebra Examples

${(\frac{32}{1024})}^{\frac{1}{5}}$

Step 1

Reduce the expression by cancelling the common factors.

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Step 1.1

Cancel the common factor of $32$ and $1024$ .

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Step 1.1.1

Factor $32$ out of $32$ .

${(\frac{32 (1)}{1024})}^{\frac{1}{5}}$

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

Factor $32$ out of $1024$ .

${(\frac{32 \cdot 1}{32 \cdot 32})}^{\frac{1}{5}}$

Step 1.1.2.2

Cancel the common factor.

${(\frac{32 \cdot 1}{32 \cdot 32})}^{\frac{1}{5}}$

Step 1.1.2.3

Rewrite the expression.

${(\frac{1}{32})}^{\frac{1}{5}}$

Step 1.2

Simplify the expression.

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Step 1.2.1

Apply the product rule to $\frac{1}{32}$ .

$\frac{1^{\frac{1}{5}}}{32^{\frac{1}{5}}}$

Step 1.2.2

One to any power is one.

$\frac{1}{32^{\frac{1}{5}}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $32$ as $2^{5}$ .

$\frac{1}{{(2^{5})}^{\frac{1}{5}}}$

Step 2.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{1}{2^{5 (\frac{1}{5})}}$

Step 2.3

Cancel the common factor of $5$ .

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Step 2.3.1

Cancel the common factor.

$\frac{1}{2^{5 (\frac{1}{5})}}$

Step 2.3.2

Rewrite the expression.

$\frac{1}{2^{1}}$

Step 2.4

Evaluate the exponent.

$\frac{1}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$