Simplify ((12p^2)/(7d^4))÷((6p^3)/(35d^2))

$\frac{12 p^{2}}{7 d^{4}} \div \frac{6 p^{3}}{35 d^{2}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{12 p^{2}}{7 d^{4}} \cdot \frac{35 d^{2}}{6 p^{3}}$

Step 2

Simplify terms.

Combine.

$\frac{12 p^{2} (35 d^{2})}{7 d^{4} (6 p^{3})}$

Cancel the common factor of $12$ and $6$ .

Factor $6$ out of $12 p^{2} (35 d^{2})$ .

$\frac{6 (2 p^{2} (35 d^{2}))}{7 d^{4} (6 p^{3})}$

Cancel the common factors.

Factor $6$ out of $7 d^{4} (6 p^{3})$ .

$\frac{6 (2 p^{2} (35 d^{2}))}{6 (7 d^{4} (p^{3}))}$

Cancel the common factor.

$\frac{6 (2 p^{2} (35 d^{2}))}{6 (7 d^{4} (p^{3}))}$

Rewrite the expression.

$\frac{2 p^{2} (35 d^{2})}{7 d^{4} (p^{3})}$

Cancel the common factor of $p^{2}$ and $p^{3}$ .

Factor $p^{2}$ out of $2 p^{2} (35 d^{2})$ .

$\frac{p^{2} (2 (35 d^{2}))}{7 d^{4} (p^{3})}$

Cancel the common factors.

Factor $p^{2}$ out of $7 d^{4} (p^{3})$ .

$\frac{p^{2} (2 (35 d^{2}))}{p^{2} (7 d^{4} (p))}$

Cancel the common factor.

$\frac{p^{2} (2 (35 d^{2}))}{p^{2} (7 d^{4} (p))}$

Rewrite the expression.

$\frac{2 (35 d^{2})}{7 d^{4} (p)}$

Cancel the common factor of $35$ and $7$ .

Factor $7$ out of $2 (35 d^{2})$ .

$\frac{7 (2 (5 d^{2}))}{7 d^{4} (p)}$

Cancel the common factors.

Factor $7$ out of $7 d^{4} (p)$ .

$\frac{7 (2 (5 d^{2}))}{7 (d^{4} (p))}$

Cancel the common factor.

$\frac{7 (2 (5 d^{2}))}{7 (d^{4} (p))}$

Rewrite the expression.

$\frac{2 (5 d^{2})}{d^{4} (p)}$

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

Factor $d^{2}$ out of $2 (5 d^{2})$ .

$\frac{d^{2} (2 \cdot (5))}{d^{4} (p)}$

Cancel the common factors.

Factor $d^{2}$ out of $d^{4} (p)$ .

$\frac{d^{2} (2 \cdot (5))}{d^{2} (d^{2} p)}$

Cancel the common factor.

$\frac{d^{2} (2 \cdot (5))}{d^{2} (d^{2} p)}$

Rewrite the expression.

$\frac{2 \cdot (5)}{d^{2} p}$

Step 3

Multiply $2$ by $5$ .

$\frac{10}{d^{2} p}$

Simplify ((12p^2)/(7d^4))÷((6p^3)/(35d^2))

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