Simplify x(3x^2)^3

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

Step 1

Apply the product rule to $3 x^{2}$ .

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

Step 2

Rewrite using the commutative property of multiplication.

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

Step 3

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

$27 x {(x^{2})}^{3}$

Step 4

Multiply the exponents in ${(x^{2})}^{3}$ .

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

$27 x \cdot x^{2 \cdot 3}$

Multiply $2$ by $3$ .

$27 x \cdot x^{6}$

Step 5

Multiply $x$ by $x^{6}$ by adding the exponents.

Move $x^{6}$ .

$27 (x^{6} x)$

Multiply $x^{6}$ by $x$ .

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

$27 (x^{6} x^{1})$

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

$27 x^{6 + 1}$

Add $6$ and $1$ .

$27 x^{7}$