Simplify (2^-7*5^5)^2

${(2^{- 7} \cdot 5^{5})}^{2}$

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

${(\frac{1}{2^{7}} \cdot 5^{5})}^{2}$

Evaluate the exponents.

Raise $2$ to the power of $7$ .

${(\frac{1}{128} \cdot 5^{5})}^{2}$

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

${(\frac{1}{128} \cdot 3125)}^{2}$

Combine $\frac{1}{128}$ and $3125$ .

${(\frac{3125}{128})}^{2}$

Simplify the expression.

Apply the product rule to $\frac{3125}{128}$ .

$\frac{3125^{2}}{128^{2}}$

Raise $3125$ to the power of $2$ .

$\frac{9765625}{128^{2}}$

Raise $128$ to the power of $2$ .

$\frac{9765625}{16384}$

The result can be shown in multiple forms.

Exact Form:

$\frac{9765625}{16384}$

Decimal Form:

$596.04644775 \dots$

Mixed Number Form:

$596 \frac{761}{16384}$