Question

Which expression is equivalent to StartFraction negative 18 a Superscript negative 2 Baseline b Superscript 5 Baseline Over Negative 12 a Superscript negative 4 Baseline b Superscript negative 6 Baseline EndFraction? Assume a not-equals 0, b not-equals 0.

StartFraction 2 a squared b Superscript 11 Baseline Over 3 EndFraction
StartFraction 2 a squared b Superscript 30 Baseline Over 3 EndFraction
StartFraction 3 a squared b Superscript 11 Baseline Over 2 EndFraction
StartFraction 3 a squared b Superscript 30 Baseline Over 2 EndFraction

Answer 1

Answer: To simplify the expression and find an equivalent form, we need to combine the exponents and simplify the coefficients. Let's break down the given expression:

StartFraction negative 18 a Superscript negative 2 Baseline b Superscript 5 Baseline Over Negative 12 a Superscript negative 4 Baseline b Superscript negative 6 Baseline EndFraction

To combine the exponents, we subtract the exponents of a and b in the denominator from the exponents of a and b in the numerator:

negative 2 - negative 4 = 2 - 4 = -2 - (-4) = -2 + 4 = 2

5 - (-6) = 5 + 6 = 11

The expression now simplifies to:

StartFraction negative 18 a squared b Superscript 11 Baseline Over negative 12 EndFraction

To further simplify, we can cancel out common factors in the numerator and denominator:

negative 18 divided by negative 12 = 3 divided by 2

Therefore, the equivalent expression is:

StartFraction 3 a squared b Superscript 11 Baseline Over 2 EndFraction

Out of the given options, the correct expression is:

StartFraction 3 a squared b Superscript 11 Baseline Over 2 EndFraction

Explanation: