Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

Evaluate the exponents.

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Step 4.1

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

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

Step 4.2

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

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

Step 5

Cancel the common factor of $2$ .

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Step 5.1

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

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

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

Step 6

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

$\frac{8}{16}$

Step 7

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

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Step 7.1

Factor $8$ out of $8$ .

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

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $8$ out of $16$ .

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

Step 7.2.2

Cancel the common factor.

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

Step 7.2.3

Rewrite the expression.

$\frac{1}{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$