Evaluate Using the Given Value 1/2a^-4b^2 for a=-2 and b=4

$\frac{1}{2} a^{- 4} b^{2}$ for $a = - 2$ and $b = 4$

Replace the variable $a$ with $- 2$ in the expression.

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

Replace the variable $b$ with $4$ in the expression.

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

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

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

Evaluate the exponents.

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

$\frac{1}{2} \cdot (\frac{1}{16} {(4)}^{2})$

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

$\frac{1}{2} \cdot (\frac{1}{16} \cdot 16)$

Cancel the common factor of $2$ .

Factor $2$ out of $\frac{1}{16} \cdot 16$ .

$\frac{1}{2} \cdot (2 (\frac{1}{16} \cdot 8))$

Cancel the common factor.

$\frac{1}{2} \cdot (2 (\frac{1}{16} \cdot 8))$

Rewrite the expression.

$\frac{1}{16} \cdot 8$

Combine $\frac{1}{16}$ and $8$ .

$\frac{8}{16}$

Cancel the common factor of $8$ and $16$ .

Factor $8$ out of $8$ .

$\frac{8 (1)}{16}$

Cancel the common factors.

Factor $8$ out of $16$ .

$\frac{8 \cdot 1}{8 \cdot 2}$

Cancel the common factor.

$\frac{8 \cdot 1}{8 \cdot 2}$

Rewrite the expression.

$\frac{1}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$