Simplify (18a^3b^4c^2)/(6a^5bc^-3)

$\frac{18 a^{3} b^{4} c^{2}}{6 a^{5} b c^{- 3}}$

Move $c^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{18 a^{3} b^{4} c^{2} c^{3}}{6 a^{5} b}$

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

Move $c^{3}$ .

$\frac{18 a^{3} b^{4} (c^{3} c^{2})}{6 a^{5} b}$

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

$\frac{18 a^{3} b^{4} c^{3 + 2}}{6 a^{5} b}$

Add $3$ and $2$ .

$\frac{18 a^{3} b^{4} c^{5}}{6 a^{5} b}$

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

Factor $6$ out of $18 a^{3} b^{4} c^{5}$ .

$\frac{6 (3 a^{3} b^{4} c^{5})}{6 a^{5} b}$

Cancel the common factors.

Factor $6$ out of $6 a^{5} b$ .

$\frac{6 (3 a^{3} b^{4} c^{5})}{6 (a^{5} b)}$

Cancel the common factor.

$\frac{6 (3 a^{3} b^{4} c^{5})}{6 (a^{5} b)}$

Rewrite the expression.

$\frac{3 a^{3} b^{4} c^{5}}{a^{5} b}$

Cancel the common factor of $a^{3}$ and $a^{5}$ .

Factor $a^{3}$ out of $3 a^{3} b^{4} c^{5}$ .

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

Cancel the common factors.

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

$\frac{a^{3} (3 b^{4} c^{5})}{a^{3} (a^{2} b)}$

Cancel the common factor.

$\frac{a^{3} (3 b^{4} c^{5})}{a^{3} (a^{2} b)}$

Rewrite the expression.

$\frac{3 b^{4} c^{5}}{a^{2} b}$

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

Factor $b$ out of $3 b^{4} c^{5}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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