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

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

Move $c^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

Multiply $c^{0}$ by $c^{2}$ by adding the exponents.

Move $c^{2}$ .

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

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

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

Add $2$ and $0$ .

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

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

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

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

Move $b$ .

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

Multiply $b$ by $b^{3}$ .

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

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

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

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

Add $1$ and $3$ .

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

Cancel the common factor of $a^{4}$ and $a^{2}$ .

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

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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