Simplify (6a^2)/(5b^2)*(45b^3)/(18a^3)

$\frac{6 a^{2}}{5 b^{2}} \cdot \frac{45 b^{3}}{18 a^{3}}$

Combine.

$\frac{6 a^{2} (45 b^{3})}{5 b^{2} (18 a^{3})}$

Cancel the common factor of $6$ and $18$ .

Factor $6$ out of $6 a^{2} (45 b^{3})$ .

$\frac{6 (a^{2} (45 b^{3}))}{5 b^{2} (18 a^{3})}$

Cancel the common factors.

Factor $6$ out of $5 b^{2} (18 a^{3})$ .

$\frac{6 (a^{2} (45 b^{3}))}{6 (5 b^{2} (3 a^{3}))}$

Cancel the common factor.

$\frac{6 (a^{2} (45 b^{3}))}{6 (5 b^{2} (3 a^{3}))}$

Rewrite the expression.

$\frac{a^{2} (45 b^{3})}{5 b^{2} (3 a^{3})}$

Cancel the common factors.

Factor $a^{2}$ out of $5 b^{2} (3 a^{3})$ .

$\frac{a^{2} (45 b^{3})}{a^{2} (5 b^{2} (3 a))}$

Cancel the common factor.

$\frac{a^{2} (45 b^{3})}{a^{2} (5 b^{2} (3 a))}$

Rewrite the expression.

$\frac{45 b^{3}}{5 b^{2} (3 a)}$

Cancel the common factor of $45$ and $5$ .

Factor $5$ out of $45 b^{3}$ .

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

Cancel the common factors.

Factor $5$ out of $5 b^{2} (3 a)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $9$ and $3$ .

Factor $3$ out of $9 b^{3}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

Factor $b^{2}$ out of $3 b^{3}$ .

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

Cancel the common factors.

Cancel the common factor.

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

Rewrite the expression.

$\frac{3 b}{a}$

Simplify (6a^2)/(5b^2)*(45b^3)/(18a^3)

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