Given:
The given expression is [tex]\frac{b^{-2}}{a b^{-3}}[/tex]
Let us assume that [tex]a \neq 0, b \neq 0[/tex]
We need to determine an expression that is equivalent to the expression [tex]\frac{b^{-2}}{a b^{-3}}[/tex]
Equivalent expression:
The equivalent expression can be determined by solving the given expression.
Hence, applying the exponent rule, [tex]\frac{x^{a}}{x^{b}}=x^{a-b}[/tex]
Thus, we get;
[tex]\frac{b^{-2}}{a b^{-3}}=\frac{b^{-2-(-3)}}{a}[/tex]
Subtracting the numbers, we get;
[tex]\frac{b^{-2}}{a b^{-3}}=\frac{b}{a}[/tex]
Thus, the equivalent expression is [tex]\frac{b}{a}[/tex]
Hence, Option D is the correct answer.
