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

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

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

Multiply $x^{2}$ by $x$ .

Raise $x$ to the power of $1$ .

${(3 \cdot 4 (x^{2} x^{1}))}^{3}$

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

${(3 \cdot 4 x^{2 + 1})}^{3}$

Add $2$ and $1$ .

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

Multiply $3$ by $4$ .

${(12 x^{3})}^{3}$

Apply the product rule to $12 x^{3}$ .

$12^{3} {(x^{3})}^{3}$

Raise $12$ to the power of $3$ .

$1728 {(x^{3})}^{3}$

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

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

$1728 x^{3 \cdot 3}$

Multiply $3$ by $3$ .

$1728 x^{9}$