Question

Fatima evaluated the expression StartFraction 4 m Superscript negative 3 Baseline n Superscript negative 2 Baseline Over m Superscript negative 1 Baseline n EndFraction, when m = negative 2 and n = 4. Her work is shown below.

StartFraction 4 m Superscript negative 3 Baseline n Superscript negative 2 Baseline Over m Superscript negative 1 Baseline n EndFraction = 4 m Superscript negative 2 Baseline n Superscript negative 3 Baseline = 4 (negative 2) Superscript negative 2 Baseline (4) Superscript negative 3 Baseline = StartFraction 1 Over 64 EndFraction times StartFraction 1 Over 64 EndFraction = StartFraction 1 Over 4,096 EndFraction

What was Fatima’s error?
She subtracted the exponents incorrectly when simplifying the expression.
She substituted the wrong values for the variables.
She did not correctly follow the order of operations by applying the exponent Negative 2 to 4 (negative 2).
She found an incorrect value for (Negative 8) Superscript negative 2 since the value should be negative.

Answer 1

Correct choice: She did not correctly follow the order of operations by applying the exponent Negative 2 to 4 (negative 2).

Explanation: After simplifying to 4 m⁻² n⁻³ and substituting m = −2, n = 4, the expression is
4 · (−2)⁻² · 4⁻³.
Fatima treated 4·(−2)⁻² as (4·(−2))⁻² = (−8)⁻² = 1/64, but (−2)⁻² = 1/4, so
4 · (1/4) · (1/64) = 1/64.
Her mistake was applying the −2 exponent to the 4 as well as to m.