Question

Which expression is equivalent to StartFraction b Superscript negative 2 Baseline Over a b Superscript negative 3 Baseline EndFraction? Assume a not-equals 0, b not-equals 0.

Answer 1

Given:

The given expression is $\frac{b^{-2}}{a b^{-3}}$

Let us assume that $a \neq 0, b \neq 0$

We need to determine an expression that is equivalent to the expression $\frac{b^{-2}}{a b^{-3}}$

Equivalent expression:

The equivalent expression can be determined by solving the given expression.

Hence, applying the exponent rule, $\frac{x^{a}}{x^{b}}=x^{a-b}$

Thus, we get;

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

Subtracting the numbers, we get;

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

Thus, the equivalent expression is $\frac{b}{a}$

Hence, Option D is the correct answer.