Simplify (5^-2*4^-4)^-2

${(5^{- 2} \cdot 4^{- 4})}^{- 2}$

Step 1

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

${(\frac{1}{5^{2}} \cdot 4^{- 4})}^{- 2}$

Step 2

Raise $5$ to the power of $2$ .

${(\frac{1}{25} \cdot 4^{- 4})}^{- 2}$

Step 3

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

${(\frac{1}{25} \cdot \frac{1}{4^{4}})}^{- 2}$

Step 4

Combine.

${(\frac{1 \cdot 1}{25 \cdot 4^{4}})}^{- 2}$

Step 5

Simplify the expression.

Multiply $1$ by $1$ .

${(\frac{1}{25 \cdot 4^{4}})}^{- 2}$

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

${(\frac{1}{25 \cdot 256})}^{- 2}$

Multiply $25$ by $256$ .

${(\frac{1}{6400})}^{- 2}$

Step 6

Change the sign of the exponent by rewriting the base as its reciprocal.

$6400^{2}$

Step 7

Raise $6400$ to the power of $2$ .

$40960000$