Answer:
Step-by-step explanation:
Writing the description in algebraic translation
[tex]\frac{b^{-2}}{ab^{-3}}[/tex]
so we have to find the expression which will be equal to [tex]\frac{b^{-2}}{ab^{-3}}[/tex].
Considering the expression
[tex]\frac{b^{-2}}{ab^{-3}}[/tex]
[tex]\mathrm{Apply\:exponent\:rule}:\quad \frac{x^a}{x^b}=x^{a-b}[/tex]
[tex]\frac{b^{-2}}{b^{-3}}=b^{-2-\left(-3\right)}[/tex]
so the expression becomes
[tex]=\frac{b^{-2-\left(-3\right)}}{a}[/tex] ∵ [tex]\frac{b^{-2}}{b^{-3}}=b^{-2-\left(-3\right)}[/tex]
[tex]\mathrm{Subtract\:the\:numbers:}\:-2-\left(-3\right)=1[/tex]
[tex]=\frac{b}{a}[/tex]
Therefore,
[tex]\frac{b^{-2}}{ab^{-3}}=\frac{b}{a}[/tex]
