Evaluate -1/(2(4)^(3/2))

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

Simplify the denominator.

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

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Add $1$ and $3$ .

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

Raise $2$ to the power of $4$ .

$- \frac{1}{16}$

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{16}$

Decimal Form:

$- 0.0625$