Simplify (6x^2)/(7x)*2/(3x^3)

$\frac{6 x^{2}}{7 x} \cdot \frac{2}{3 x^{3}}$

Step 1

Combine.

$\frac{6 x^{2} \cdot 2}{7 x (3 x^{3})}$

Step 2

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

Move $x^{3}$ .

$\frac{6 x^{2} \cdot 2}{7 (x^{3} x) \cdot 3}$

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

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

$\frac{6 x^{2} \cdot 2}{7 (x^{3} x^{1}) \cdot 3}$

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

$\frac{6 x^{2} \cdot 2}{7 x^{3 + 1} \cdot 3}$

$\frac{6 x^{2} \cdot 2}{7 x^{3 + 1} \cdot 3}$

Add $3$ and $1$ .

$\frac{6 x^{2} \cdot 2}{7 x^{4} \cdot 3}$

$\frac{6 x^{2} \cdot 2}{7 x^{4} \cdot 3}$

Step 3

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

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

$\frac{3 (2 x^{2} \cdot 2)}{7 x^{4} \cdot 3}$

Cancel the common factors.

Factor $3$ out of $7 x^{4} \cdot 3$ .

$\frac{3 (2 x^{2} \cdot 2)}{3 \cdot (7 x^{4})}$

Cancel the common factor.

$\frac{3 (2 x^{2} \cdot 2)}{3 \cdot (7 x^{4})}$

Rewrite the expression.

$\frac{2 x^{2} \cdot 2}{7 x^{4}}$

$\frac{2 x^{2} \cdot 2}{7 x^{4}}$

$\frac{2 x^{2} \cdot 2}{7 x^{4}}$

Step 4

Cancel the common factor of $x^{2}$ and $x^{4}$ .

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

$\frac{x^{2} (2 \cdot 2)}{7 x^{4}}$

Cancel the common factors.

Factor $x^{2}$ out of $7 x^{4}$ .

$\frac{x^{2} (2 \cdot 2)}{x^{2} (7 x^{2})}$

Cancel the common factor.

$\frac{x^{2} (2 \cdot 2)}{x^{2} (7 x^{2})}$

Rewrite the expression.

$\frac{2 \cdot 2}{7 x^{2}}$

$\frac{2 \cdot 2}{7 x^{2}}$

$\frac{2 \cdot 2}{7 x^{2}}$

Step 5

Multiply $2$ by $2$ .

$\frac{4}{7 x^{2}}$

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