Evaluate 1/(4(16)^(3/4))

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

Step 1

Simplify the denominator.

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

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

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

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

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

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

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

Cancel the common factor of $4$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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:

$0.03125$