Algebra Examples

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

Step 1

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

$256 \cdot {(4^{- 2})}^{4}$

Step 2

Multiply the exponents in ${(4^{- 2})}^{4}$ .

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Step 2.1

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

$256 \cdot 4^{- 2 \cdot 4}$

Step 2.2

Multiply $- 2$ by $4$ .

$256 \cdot 4^{- 8}$

Step 3

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

$256 \cdot \frac{1}{4^{8}}$

Step 4

Raise $4$ to the power of $8$ .

$256 \cdot \frac{1}{65536}$

Step 5

Cancel the common factor of $256$ .

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Step 5.1

Factor $256$ out of $65536$ .

$256 \cdot \frac{1}{256 (256)}$

Step 5.2

Cancel the common factor.

$256 \cdot \frac{1}{256 \cdot 256}$

Step 5.3

Rewrite the expression.

$\frac{1}{256}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{256}$

Decimal Form:

$0.00390625$