Simplify (2x^4)(3x^6)(-2x)x^3

$(2 x^{4}) (3 x^{6}) (- 2 x) x^{3}$

Step 1

Multiply $x^{4}$ by $x^{6}$ by adding the exponents.

Move $x^{6}$ .

$2 (x^{6} x^{4}) \cdot 3 (- 2 x) x^{3}$

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

$2 x^{6 + 4} \cdot 3 (- 2 x) x^{3}$

Add $6$ and $4$ .

$2 x^{10} \cdot 3 (- 2 x) x^{3}$

Step 2

Multiply $x^{10}$ by $x$ by adding the exponents.

Move $x$ .

$2 (x \cdot x^{10}) \cdot 3 \cdot - 2 x^{3}$

Multiply $x$ by $x^{10}$ .

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

$2 (x^{1} x^{10}) \cdot 3 \cdot - 2 x^{3}$

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

$2 x^{1 + 10} \cdot 3 \cdot - 2 x^{3}$

Add $1$ and $10$ .

$2 x^{11} \cdot 3 \cdot - 2 x^{3}$

Step 3

Multiply $x^{11}$ by $x^{3}$ by adding the exponents.

Move $x^{3}$ .

$2 (x^{3} x^{11}) \cdot 3 \cdot - 2$

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

$2 x^{3 + 11} \cdot 3 \cdot - 2$

Add $3$ and $11$ .

$2 x^{14} \cdot 3 \cdot - 2$

Step 4

Multiply $3$ by $2$ .

$6 x^{14} \cdot - 2$

Step 5

Multiply $- 2$ by $6$ .

$- 12 x^{14}$