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

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

Multiply the exponents in ${(5^{2})}^{4}$ .

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

$5^{2 \cdot 4} \cdot 5^{5}$

Multiply $2$ by $4$ .

$5^{8} \cdot 5^{5}$

Multiply $5^{8}$ by $5^{5}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$5^{8 + 5}$

Add $8$ and $5$ .

$5^{13}$

Raise $5$ to the power of $13$ .

$1220703125$