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:

I got it correct on edge

Answer 2

`(b)/(a)`

Explanation:

We want to find an expression that is equivalent to :
`(b^(-2))/(ab^(-3))`

We need to use the following rule of exponents.
`a^(n)=(1)/(a^(-n))`

We apply this rule to send the
`b^(-3)`in the denominator to the numerator to get:

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

Recall also the product rule of exponents:
`b^m* b^n=b^(m+n)`

`\implies (b^(-2)*b^(3))/(a)=(b^(-2+3))/(a)`

We finally simplify to get:

`(b^1)/(a)=(b)/(a)`