Algebra Examples

$2 {(2 \sqrt{4})}^{- 2}$

Step 1

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

$2 {(2 \sqrt{2^{2}})}^{- 2}$

Step 2

Pull terms out from under the radical, assuming positive real numbers.

$2 {(2 \cdot 2)}^{- 2}$

Step 3

Multiply $2$ by $2$ .

$2 \cdot 4^{- 2}$

Step 4

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

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

Step 5

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

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

Step 6

Cancel the common factor of $2$ .

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Step 6.1

Factor $2$ out of $16$ .

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

Step 6.2

Cancel the common factor.

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

Step 6.3

Rewrite the expression.

$\frac{1}{8}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{8}$

Decimal Form:

$0.125$