Simplify ((12x)/(14x^5))÷((3x^2)/(7x^3))

$\frac{12 x}{14 x^{5}} \div \frac{3 x^{2}}{7 x^{3}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{12 x}{14 x^{5}} \cdot \frac{7 x^{3}}{3 x^{2}}$

Step 2

Combine.

$\frac{12 x (7 x^{3})}{14 x^{5} (3 x^{2})}$

Step 3

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

Move $x^{3}$ .

$\frac{12 (x^{3} x) \cdot 7}{14 x^{5} (3 x^{2})}$

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

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

$\frac{12 (x^{3} x^{1}) \cdot 7}{14 x^{5} (3 x^{2})}$

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

$\frac{12 x^{3 + 1} \cdot 7}{14 x^{5} (3 x^{2})}$

Add $3$ and $1$ .

$\frac{12 x^{4} \cdot 7}{14 x^{5} (3 x^{2})}$

Step 4

Multiply $x^{5}$ by $x^{2}$ by adding the exponents.

Move $x^{2}$ .

$\frac{12 x^{4} \cdot 7}{14 (x^{2} x^{5}) \cdot 3}$

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

$\frac{12 x^{4} \cdot 7}{14 x^{2 + 5} \cdot 3}$

Add $2$ and $5$ .

$\frac{12 x^{4} \cdot 7}{14 x^{7} \cdot 3}$

Step 5

Cancel the common factor of $12$ and $14$ .

Factor $2$ out of $12 x^{4} \cdot 7$ .

$\frac{2 (6 x^{4} \cdot 7)}{14 x^{7} \cdot 3}$

Cancel the common factors.

Factor $2$ out of $14 x^{7} \cdot 3$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 6

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

Factor $3$ out of $6 x^{4} \cdot 7$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 7

Cancel the common factor of $x^{4}$ and $x^{7}$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 8

Cancel the common factor of $7$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify ((12x)/(14x^5))÷((3x^2)/(7x^3))

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