Questions: Which shows the following expression after the negative exponents have been eliminated? a^3 b^-2 / a b^-1, a ≠ 0, b ≠ 0 a^3 b^4 / a b^2 a b^4 / a^3 b^2 -a^3 b^4 / a b^2 a^3 b^-4 / a b^-2

Solution Steps

The given expression is

\[ \frac{a^{3} b^{-2}}{a b^{-1}} \]

First, simplify the expression by handling the negative exponents. Recall that \(b^{-n} = \frac{1}{b^n}\).

Rewrite the expression by eliminating the negative exponents:

\[ \frac{a^{3} \cdot \frac{1}{b^{2}}}{a \cdot \frac{1}{b^{-1}}} = \frac{a^{3}}{b^{2}} \cdot \frac{b}{a} \]

Now, simplify the fraction:

\[ = \frac{a^{3} \cdot b}{a \cdot b^{2}} = \frac{a^{3-1} \cdot b^{1-2}}{1} = \frac{a^{2}}{b} \]

Final Answer