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

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

Multiply $5^{3}$ by $5^{2}$ by adding the exponents.

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

${(5^{3 + 2})}^{4}$

Add $3$ and $2$ .

${(5^{5})}^{4}$

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

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

$5^{5 \cdot 4}$

Multiply $5$ by $4$ .

$5^{20}$

Raise $5$ to the power of $20$ .

$95367431640625$