Simplify (5^32^4)^2(5^-22^5)

${(5^{3} \cdot 2^{4})}^{2} (5^{- 2} \cdot 2^{5})$

Raise $5$ to the power of $3$ .

${(125 \cdot 2^{4})}^{2} (5^{- 2} \cdot 2^{5})$

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

${(125 \cdot 16)}^{2} (5^{- 2} \cdot 2^{5})$

Multiply $125$ by $16$ .

$2000^{2} (5^{- 2} \cdot 2^{5})$

Raise $2000$ to the power of $2$ .

$4000000 (5^{- 2} \cdot 2^{5})$

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

$4000000 (\frac{1}{5^{2}} \cdot 2^{5})$

Evaluate the exponents.

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

$4000000 (\frac{1}{25} \cdot 2^{5})$

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

$4000000 (\frac{1}{25} \cdot 32)$

Combine $\frac{1}{25}$ and $32$ .

$4000000 (\frac{32}{25})$

Cancel the common factor of $25$ .

Factor $25$ out of $4000000$ .

$25 (160000) \frac{32}{25}$

Cancel the common factor.

$25 \cdot 160000 \frac{32}{25}$

Rewrite the expression.

$160000 \cdot 32$

Multiply $160000$ by $32$ .

$5120000$

Simplify (5^3*2^4)^2(5^-2*2^5)