Simplify ((6bc^3)(3b^5c^2))/((5b^5c^2)(2b^3c^6))

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

Step 1

Multiply $b$ by $b^{5}$ by adding the exponents.

Move $b^{5}$ .

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

Multiply $b^{5}$ by $b$ .

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

$\frac{6 (b^{5} b^{1}) c^{3} (3 c^{2})}{(5 b^{5} c^{2}) (2 b^{3} c^{6})}$

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

$\frac{6 b^{5 + 1} c^{3} (3 c^{2})}{(5 b^{5} c^{2}) (2 b^{3} c^{6})}$

Add $5$ and $1$ .

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

Step 2

Multiply $c^{3}$ by $c^{2}$ by adding the exponents.

Move $c^{2}$ .

$\frac{6 b^{6} (c^{2} c^{3}) \cdot 3}{(5 b^{5} c^{2}) (2 b^{3} c^{6})}$

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

$\frac{6 b^{6} c^{2 + 3} \cdot 3}{(5 b^{5} c^{2}) (2 b^{3} c^{6})}$

Add $2$ and $3$ .

$\frac{6 b^{6} c^{5} \cdot 3}{(5 b^{5} c^{2}) (2 b^{3} c^{6})}$

Step 3

Multiply $b^{5}$ by $b^{3}$ by adding the exponents.

Move $b^{3}$ .

$\frac{6 b^{6} c^{5} \cdot 3}{5 (b^{3} b^{5}) c^{2} (2 c^{6})}$

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

$\frac{6 b^{6} c^{5} \cdot 3}{5 b^{3 + 5} c^{2} (2 c^{6})}$

Add $3$ and $5$ .

$\frac{6 b^{6} c^{5} \cdot 3}{5 b^{8} c^{2} (2 c^{6})}$

Step 4

Multiply $c^{2}$ by $c^{6}$ by adding the exponents.

Move $c^{6}$ .

$\frac{6 b^{6} c^{5} \cdot 3}{5 b^{8} (c^{6} c^{2}) \cdot 2}$

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

$\frac{6 b^{6} c^{5} \cdot 3}{5 b^{8} c^{6 + 2} \cdot 2}$

Add $6$ and $2$ .

$\frac{6 b^{6} c^{5} \cdot 3}{5 b^{8} c^{8} \cdot 2}$

Step 5

Cancel the common factor of $6$ and $2$ .

Factor $2$ out of $6 b^{6} c^{5} \cdot 3$ .

$\frac{2 (3 b^{6} c^{5} \cdot 3)}{5 b^{8} c^{8} \cdot 2}$

Cancel the common factors.

Factor $2$ out of $5 b^{8} c^{8} \cdot 2$ .

$\frac{2 (3 b^{6} c^{5} \cdot 3)}{2 \cdot (5 b^{8} c^{8})}$

Cancel the common factor.

$\frac{2 (3 b^{6} c^{5} \cdot 3)}{2 \cdot (5 b^{8} c^{8})}$

Rewrite the expression.

$\frac{3 b^{6} c^{5} \cdot 3}{5 b^{8} c^{8}}$

Step 6

Cancel the common factor of $b^{6}$ and $b^{8}$ .

Factor $b^{6}$ out of $3 b^{6} c^{5} \cdot 3$ .

$\frac{b^{6} (3 c^{5} \cdot 3)}{5 b^{8} c^{8}}$

Cancel the common factors.

Factor $b^{6}$ out of $5 b^{8} c^{8}$ .

$\frac{b^{6} (3 c^{5} \cdot 3)}{b^{6} (5 b^{2} c^{8})}$

Cancel the common factor.

$\frac{b^{6} (3 c^{5} \cdot 3)}{b^{6} (5 b^{2} c^{8})}$

Rewrite the expression.

$\frac{3 c^{5} \cdot 3}{5 b^{2} c^{8}}$

Step 7

Cancel the common factor of $c^{5}$ and $c^{8}$ .

Factor $c^{5}$ out of $3 c^{5} \cdot 3$ .

$\frac{c^{5} (3 \cdot 3)}{5 b^{2} c^{8}}$

Cancel the common factors.

Factor $c^{5}$ out of $5 b^{2} c^{8}$ .

$\frac{c^{5} (3 \cdot 3)}{c^{5} (5 b^{2} c^{3})}$

Cancel the common factor.

$\frac{c^{5} (3 \cdot 3)}{c^{5} (5 b^{2} c^{3})}$

Rewrite the expression.

$\frac{3 \cdot 3}{5 b^{2} c^{3}}$

Step 8

Multiply $3$ by $3$ .

$\frac{9}{5 b^{2} c^{3}}$

Simplify ((6bc^3)(3b^5c^2))/((5b^5c^2)(2b^3c^6))

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