Simplify ((18ab)/(15b^5))÷((2a)/(3b))

$\frac{18 a b}{15 b^{5}} \div \frac{2 a}{3 b}$

To divide by a fraction, multiply by its reciprocal.

$\frac{18 a b}{15 b^{5}} \cdot \frac{3 b}{2 a}$

Cancel the common factor of $2 a$ .

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Factor $2 a$ out of $18 a b$ .

$\frac{2 a (9 b)}{15 b^{5}} \cdot \frac{3 b}{2 a}$

Cancel the common factor.

$\frac{2 a (9 b)}{15 b^{5}} \cdot \frac{3 b}{2 a}$

Rewrite the expression.

$\frac{9 b}{15 b^{5}} (3 b)$

Cancel the common factor of $3 b$ .

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Factor $3 b$ out of $15 b^{5}$ .

$\frac{9 b}{3 b (5 b^{4})} (3 b)$

Cancel the common factor.

$\frac{9 b}{3 b (5 b^{4})} (3 b)$

Rewrite the expression.

$\frac{9 b}{5 b^{4}}$

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

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Factor $b$ out of $9 b$ .

$\frac{b \cdot 9}{5 b^{4}}$

Cancel the common factors.

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Factor $b$ out of $5 b^{4}$ .

$\frac{b \cdot 9}{b (5 b^{3})}$

Cancel the common factor.

$\frac{b \cdot 9}{b (5 b^{3})}$

Rewrite the expression.

$\frac{9}{5 b^{3}}$

Simplify ((18ab)/(15b^5))÷((2a)/(3b))

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