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

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

Multiply the exponents in ${(5^{3})}^{4}$ .

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

$5^{3 \cdot 4} \cdot 5^{5}$

Multiply $3$ by $4$ .

$5^{12} \cdot 5^{5}$

Multiply $5^{12}$ by $5^{5}$ by adding the exponents.

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

$5^{12 + 5}$

Add $12$ and $5$ .

$5^{17}$

Raise $5$ to the power of $17$ .

$762939453125$