Simplify x^2(5x^3)^3

$x^{2} {(5 x^{3})}^{3}$

Apply the product rule to $5 x^{3}$ .

$x^{2} (5^{3} {(x^{3})}^{3})$

Rewrite using the commutative property of multiplication.

$5^{3} x^{2} {(x^{3})}^{3}$

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

$125 x^{2} {(x^{3})}^{3}$

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

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

$125 x^{2} x^{3 \cdot 3}$

Multiply $3$ by $3$ .

$125 x^{2} x^{9}$

Multiply $x^{2}$ by $x^{9}$ by adding the exponents.

Move $x^{9}$ .

$125 (x^{9} x^{2})$

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

$125 x^{9 + 2}$

Add $9$ and $2$ .

$125 x^{11}$