Simplify (4a^2bc^3)/(24b^-2)

$\frac{4 a^{2} b c^{3}}{24 b^{- 2}}$

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

$\frac{4 a^{2} b c^{3} b^{2}}{24}$

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

Move $b^{2}$ .

$\frac{4 a^{2} (b^{2} b) c^{3}}{24}$

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

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

$\frac{4 a^{2} (b^{2} b^{1}) c^{3}}{24}$

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

$\frac{4 a^{2} b^{2 + 1} c^{3}}{24}$

Add $2$ and $1$ .

$\frac{4 a^{2} b^{3} c^{3}}{24}$

Cancel the common factor of $4$ and $24$ .

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

$\frac{4 (a^{2} b^{3} c^{3})}{24}$

Cancel the common factors.

Factor $4$ out of $24$ .

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

Cancel the common factor.

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

Rewrite the expression.

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