Simplify (4a^-3b^-4)/(4a^3)

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

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

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

Move $b^{- 4}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

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

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

Move $a^{3}$ .

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

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

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

Add $3$ and $3$ .

$\frac{4}{4 a^{6} b^{4}}$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{4 a^{6} b^{4}}$

Rewrite the expression.

$\frac{1}{a^{6} b^{4}}$