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

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

Step 1

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

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

Step 2

Multiply $b^{2}$ by $b^{4}$ by adding the exponents.

Move $b^{4}$ .

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

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

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

Add $4$ and $2$ .

$\frac{a^{3}}{4 b^{6}}$