Simplify (5a)/(12bc^2)*(18b^2c^2)/(15a^3)

$\frac{5 a}{12 b c^{2}} \cdot \frac{18 b^{2} c^{2}}{15 a^{3}}$

Step 1

Combine.

$\frac{5 a (18 b^{2} c^{2})}{12 b c^{2} (15 a^{3})}$

Step 2

Cancel the common factor of $5$ and $15$ .

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

$\frac{5 (a (18 b^{2} c^{2}))}{12 b c^{2} (15 a^{3})}$

Cancel the common factors.

Factor $5$ out of $12 b c^{2} (15 a^{3})$ .

$\frac{5 (a (18 b^{2} c^{2}))}{5 (12 b c^{2} (3 a^{3}))}$

Cancel the common factor.

$\frac{5 (a (18 b^{2} c^{2}))}{5 (12 b c^{2} (3 a^{3}))}$

Rewrite the expression.

$\frac{a (18 b^{2} c^{2})}{12 b c^{2} (3 a^{3})}$

Step 3

Cancel the common factors.

Factor $a$ out of $12 b c^{2} (3 a^{3})$ .

$\frac{a (18 b^{2} c^{2})}{a (12 b c^{2} (3 a^{2}))}$

Cancel the common factor.

$\frac{a (18 b^{2} c^{2})}{a (12 b c^{2} (3 a^{2}))}$

Rewrite the expression.

$\frac{18 b^{2} c^{2}}{12 b c^{2} (3 a^{2})}$

Step 4

Cancel the common factor of $18$ and $12$ .

Factor $6$ out of $18 b^{2} c^{2}$ .

$\frac{6 (3 b^{2} c^{2})}{12 b c^{2} (3 a^{2})}$

Cancel the common factors.

Factor $6$ out of $12 b c^{2} (3 a^{2})$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 5

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 6

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

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 7

Cancel the common factor of $c^{2}$ .

Cancel the common factor.

$\frac{b c^{2}}{2 c^{2} a^{2}}$

Rewrite the expression.

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

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

Simplify (5a)/(12bc^2)*(18b^2c^2)/(15a^3)

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