Algebra Examples

${(\frac{1}{4})}^{\frac{5}{2}}$

Step 1

Simplify the expression.

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Step 1.1

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

$\frac{1^{\frac{5}{2}}}{4^{\frac{5}{2}}}$

Step 1.2

One to any power is one.

$\frac{1}{4^{\frac{5}{2}}}$

Step 2

Simplify the denominator.

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Step 2.1

Rewrite $4$ as $2^{2}$ .

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

Step 2.2

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

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

Step 2.3

Cancel the common factor of $2$ .

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Step 2.3.1

Cancel the common factor.

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

Step 2.3.2

Rewrite the expression.

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

Step 2.4

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

$\frac{1}{32}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{32}$

Decimal Form:

$0.03125$