Simplify ((6a^3)/(5b))/((21a)/(10b^2))

$\frac{\frac{6 a^{3}}{5 b}}{\frac{21 a}{10 b^{2}}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{6 a^{3}}{5 b} \cdot \frac{10 b^{2}}{21 a}$

Step 2

Combine.

$\frac{6 a^{3} (10 b^{2})}{5 b (21 a)}$

Step 3

Cancel the common factor of $6$ and $21$ .

Factor $3$ out of $6 a^{3} (10 b^{2})$ .

$\frac{3 (2 a^{3} (10 b^{2}))}{5 b (21 a)}$

Cancel the common factors.

Factor $3$ out of $5 b (21 a)$ .

$\frac{3 (2 a^{3} (10 b^{2}))}{3 (5 b (7 a))}$

Cancel the common factor.

$\frac{3 (2 a^{3} (10 b^{2}))}{3 (5 b (7 a))}$

Rewrite the expression.

$\frac{2 a^{3} (10 b^{2})}{5 b (7 a)}$

Step 4

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

Factor $a$ out of $2 a^{3} (10 b^{2})$ .

$\frac{a (2 a^{2} (10 b^{2}))}{5 b (7 a)}$

Cancel the common factors.

Factor $a$ out of $5 b (7 a)$ .

$\frac{a (2 a^{2} (10 b^{2}))}{a (5 b \cdot (7))}$

Cancel the common factor.

$\frac{a (2 a^{2} (10 b^{2}))}{a (5 b \cdot (7))}$

Rewrite the expression.

$\frac{2 a^{2} (10 b^{2})}{5 b \cdot (7)}$

Step 5

Cancel the common factor of $10$ and $5$ .

Factor $5$ out of $2 a^{2} (10 b^{2})$ .

$\frac{5 (2 a^{2} (2 b^{2}))}{5 b \cdot (7)}$

Cancel the common factors.

Factor $5$ out of $5 b \cdot (7)$ .

$\frac{5 (2 a^{2} (2 b^{2}))}{5 (b \cdot (7))}$

Cancel the common factor.

$\frac{5 (2 a^{2} (2 b^{2}))}{5 (b \cdot (7))}$

Rewrite the expression.

$\frac{2 a^{2} (2 b^{2})}{b \cdot (7)}$

Step 6

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

Factor $b$ out of $2 a^{2} (2 b^{2})$ .

$\frac{b (2 a^{2} (2 b))}{b \cdot (7)}$

Cancel the common factors.

Factor $b$ out of $b \cdot (7)$ .

$\frac{b (2 a^{2} (2 b))}{b (7)}$

Cancel the common factor.

$\frac{b (2 a^{2} (2 b))}{b \cdot 7}$

Rewrite the expression.

$\frac{2 a^{2} (2 b)}{7}$

Step 7

Multiply $2$ by $2$ .

$\frac{4 a^{2} b}{7}$

Simplify ((6a^3)/(5b))/((21a)/(10b^2))

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