Evaluate 4^4*(4^-2)^4

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

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

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

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

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

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

Multiply $- 2$ by $4$ .

$256 \cdot 4^{- 8}$

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

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

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

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

Cancel the common factor of $256$ .

Factor $256$ out of $65536$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{256}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{256}$

Decimal Form:

$0.00390625$