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

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

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

Move $x^{2}$ .

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

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

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

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

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

$2 x^{2 + 1} \cdot 3 x$

Add $2$ and $1$ .

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

Multiply $x^{3}$ by $x$ by adding the exponents.

Move $x$ .

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

Multiply $x$ by $x^{3}$ .

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

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

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

$2 x^{1 + 3} \cdot 3$

Add $1$ and $3$ .

$2 x^{4} \cdot 3$

Multiply $3$ by $2$ .

$6 x^{4}$