Answer:
[tex]\frac{b}{a}[/tex]
Step-by-step explanation:
We want to find an expression that is equivalent to : [tex]\frac{b^{-2}}{ab^{-3}}[/tex]
We need to use the following rule of exponents. [tex]a^{n}=\frac{1}{a^{-n}}[/tex]
We apply this rule to send the [tex]b^{-3}[/tex]in the denominator to the numerator to get:
[tex]\frac{b^{-2}*b^{3}}{a}[/tex]
Recall also the product rule of exponents: [tex]b^m\times b^n=b^{m+n}[/tex]
[tex]\implies \frac{b^{-2}*b^{3}}{a}=\frac{b^{-2+3}}{a}[/tex]
We finally simplify to get:
[tex]\frac{b^1}{a}=\frac{b}{a}[/tex]
