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

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

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

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

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

Move $b^{2}$ .

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

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

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

Add $2$ and $3$ .

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

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

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

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

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

Simplify the numerator.

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

Move $a^{2}$ .

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

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

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

Add $2$ and $3$ .

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

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

Move $d^{3}$ .

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

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

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

$\frac{a^{5} c^{4} (d^{3} d^{1})}{b^{5} c^{2}}$

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

$\frac{a^{5} c^{4} d^{3 + 1}}{b^{5} c^{2}}$

Add $3$ and $1$ .

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

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

Factor $c^{2}$ out of $a^{5} c^{4} d^{4}$ .

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

Cancel the common factors.

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

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

Cancel the common factor.

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

Rewrite the expression.

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