Evaluate 1/2(16)^(-1/2)

$\frac{1}{2} {(16)}^{- \frac{1}{2}}$

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Combine fractions.

Combine.

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

Multiply $1$ by $1$ .

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

Simplify the denominator.

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

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

Multiply the exponents in ${(2^{4})}^{\frac{1}{2}}$ .

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

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

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Add $1$ and $2$ .

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

Raise $2$ to the power of $3$ .

$\frac{1}{8}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{8}$

Decimal Form:

$0.125$