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

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

Step 1

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

Move $x$ .

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

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

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

$\frac{2 (x^{1} x^{2}) \cdot 6}{(3 x) (4 x^{2})}$

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

$\frac{2 x^{1 + 2} \cdot 6}{(3 x) (4 x^{2})}$

Add $1$ and $2$ .

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

Step 2

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

Move $x^{2}$ .

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

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

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

$\frac{2 x^{3} \cdot 6}{3 (x^{2} x^{1}) \cdot 4}$

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

$\frac{2 x^{3} \cdot 6}{3 x^{2 + 1} \cdot 4}$

Add $2$ and $1$ .

$\frac{2 x^{3} \cdot 6}{3 x^{3} \cdot 4}$

Step 3

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2 x^{3} \cdot 6$ .

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

Cancel the common factors.

Factor $2$ out of $3 x^{3} \cdot 4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{x^{3} \cdot 6}{3 x^{3} \cdot 2}$

Step 4

Cancel the common factor of $x^{3}$ .

Cancel the common factor.

$\frac{x^{3} \cdot 6}{3 x^{3} \cdot 2}$

Rewrite the expression.

$\frac{6}{3 \cdot 2}$

Step 5

Cancel the common factor of $6$ and $3$ .

Factor $3$ out of $6$ .

$\frac{3 \cdot 2}{3 \cdot 2}$

Cancel the common factors.

Factor $3$ out of $3 \cdot 2$ .

$\frac{3 \cdot 2}{3 (2)}$

Cancel the common factor.

$\frac{3 \cdot 2}{3 \cdot 2}$

Rewrite the expression.

$\frac{2}{2}$

Step 6

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{2}$

Rewrite the expression.

$1$

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

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