Simplify (4a^3b^2c^0)/(2ab^-1)

$\frac{4 a^{3} b^{2} c^{0}}{2 a b^{- 1}}$

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

$\frac{4 a^{3} b^{2} c^{0} b}{2 a}$

Simplify the numerator.

Multiply $b^{2}$ by $b$ by adding the exponents.

Move $b$ .

$\frac{4 a^{3} (b \cdot b^{2}) c^{0}}{2 a}$

Multiply $b$ by $b^{2}$ .

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

$\frac{4 a^{3} (b^{1} b^{2}) c^{0}}{2 a}$

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

$\frac{4 a^{3} b^{1 + 2} c^{0}}{2 a}$

Add $1$ and $2$ .

$\frac{4 a^{3} b^{3} c^{0}}{2 a}$

Simplify $4 a^{3} b^{3} c^{0}$ .

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

Cancel the common factor of $4$ and $2$ .

Factor $2$ out of $4 a^{3} b^{3}$ .

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

Cancel the common factors.

Factor $2$ out of $2 a$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

Cancel the common factors.

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

$\frac{a (2 a^{2} b^{3})}{a^{1}}$

Factor $a$ out of $a^{1}$ .

$\frac{a (2 a^{2} b^{3})}{a \cdot 1}$

Cancel the common factor.

$\frac{a (2 a^{2} b^{3})}{a \cdot 1}$

Rewrite the expression.

$\frac{2 a^{2} b^{3}}{1}$

Divide $2 a^{2} b^{3}$ by $1$ .

$2 a^{2} b^{3}$