Simplify (45a^2b^5)/(8cb)*(32a^4c^2)/(9a^7b^4)

$\frac{45 a^{2} b^{5}}{8 c b} \cdot \frac{32 a^{4} c^{2}}{9 a^{7} b^{4}}$

Combine.

$\frac{45 a^{2} b^{5} (32 a^{4} c^{2})}{8 c b (9 a^{7} b^{4})}$

Multiply $a^{2}$ by $a^{4}$ by adding the exponents.

Move $a^{4}$ .

$\frac{45 (a^{4} a^{2}) b^{5} (32 c^{2})}{8 c b (9 a^{7} b^{4})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{45 a^{4 + 2} b^{5} (32 c^{2})}{8 c b (9 a^{7} b^{4})}$

Add $4$ and $2$ .

$\frac{45 a^{6} b^{5} (32 c^{2})}{8 c b (9 a^{7} b^{4})}$

Multiply $b$ by $b^{4}$ by adding the exponents.

Move $b^{4}$ .

$\frac{45 a^{6} b^{5} (32 c^{2})}{8 c (b^{4} b) (9 a^{7})}$

Multiply $b^{4}$ by $b$ .

Raise $b$ to the power of $1$ .

$\frac{45 a^{6} b^{5} (32 c^{2})}{8 c (b^{4} b^{1}) (9 a^{7})}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{45 a^{6} b^{5} (32 c^{2})}{8 c b^{4 + 1} (9 a^{7})}$

Add $4$ and $1$ .

$\frac{45 a^{6} b^{5} (32 c^{2})}{8 c b^{5} (9 a^{7})}$

Cancel the common factor of $45$ and $9$ .

Factor $9$ out of $45 a^{6} b^{5} (32 c^{2})$ .

$\frac{9 (5 a^{6} b^{5} (32 c^{2}))}{8 c b^{5} (9 a^{7})}$

Cancel the common factors.

Factor $9$ out of $8 c b^{5} (9 a^{7})$ .

$\frac{9 (5 a^{6} b^{5} (32 c^{2}))}{9 (8 c b^{5} (a^{7}))}$

Cancel the common factor.

$\frac{9 (5 a^{6} b^{5} (32 c^{2}))}{9 (8 c b^{5} (a^{7}))}$

Rewrite the expression.

$\frac{5 a^{6} b^{5} (32 c^{2})}{8 c b^{5} (a^{7})}$

Cancel the common factor of $a^{6}$ and $a^{7}$ .

Factor $a^{6}$ out of $5 a^{6} b^{5} (32 c^{2})$ .

$\frac{a^{6} (5 b^{5} (32 c^{2}))}{8 c b^{5} (a^{7})}$

Cancel the common factors.

Factor $a^{6}$ out of $8 c b^{5} (a^{7})$ .

$\frac{a^{6} (5 b^{5} (32 c^{2}))}{a^{6} (8 c b^{5} (a))}$

Cancel the common factor.

$\frac{a^{6} (5 b^{5} (32 c^{2}))}{a^{6} (8 c b^{5} (a))}$

Rewrite the expression.

$\frac{5 b^{5} (32 c^{2})}{8 c b^{5} (a)}$

Cancel the common factor of $b^{5}$ .

Cancel the common factor.

$\frac{5 b^{5} (32 c^{2})}{8 c b^{5} a}$

Rewrite the expression.

$\frac{5 (32 c^{2})}{8 c (a)}$

Cancel the common factor of $32$ and $8$ .

Factor $8$ out of $5 (32 c^{2})$ .

$\frac{8 (5 (4 c^{2}))}{8 c (a)}$

Cancel the common factors.

Factor $8$ out of $8 c (a)$ .

$\frac{8 (5 (4 c^{2}))}{8 (c (a))}$

Cancel the common factor.

$\frac{8 (5 (4 c^{2}))}{8 (c (a))}$

Rewrite the expression.

$\frac{5 (4 c^{2})}{c (a)}$

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

Factor $c$ out of $5 (4 c^{2})$ .

$\frac{c (5 (4 c))}{c (a)}$

Cancel the common factors.

Cancel the common factor.

$\frac{c (5 (4 c))}{c a}$

Rewrite the expression.

$\frac{5 (4 c)}{a}$

Multiply $5$ by $4$ .

$\frac{20 c}{a}$

Simplify (45a^2b^5)/(8cb)*(32a^4c^2)/(9a^7b^4)

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