Algebra Examples

$\frac{1}{4 {(16)}^{\frac{3}{4}}}$

Step 1

Simplify the denominator.

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Step 1.1

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

$\frac{1}{2^{2} \cdot 16^{\frac{3}{4}}}$

Step 1.2

Rewrite $16$ as $2^{4}$ .

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

Step 1.3

Multiply the exponents in ${(2^{4})}^{\frac{3}{4}}$ .

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Step 1.3.1

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

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

Step 1.3.2

Cancel the common factor of $4$ .

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Step 1.3.2.1

Cancel the common factor.

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

Step 1.3.2.2

Rewrite the expression.

$\frac{1}{2^{2} \cdot 2^{3}}$

Step 1.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{1}{2^{2 + 3}}$

Step 1.5

Add $2$ and $3$ .

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

Step 2

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:

$0.03125$