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

d

Explanation:

Answer 2

Given:

The given expression is
`(b^(-2))/(a b^(-3))`

Let us assume that
`a \\eq 0, b \\eq 0`

We need to determine an expression that is equivalent to the expression
`(b^(-2))/(a b^(-3))`

Equivalent expression:

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

Hence, applying the exponent rule,
`(x^(a))/(x^(b))=x^(a-b)`

Thus, we get;

`(b^(-2))/(a b^(-3))=(b^(-2-(-3)))/(a)`

Subtracting the numbers, we get;

`(b^(-2))/(a b^(-3))=(b)/(a)`

Thus, the equivalent expression is
`(b)/(a)`

Hence, Option D is the correct answer.