Question

Analyzing Work of Simplifying an Expression
Owen simplified the expression r-8 s-5.


r−8s−5 =
1
r8
⋅ s5 =
s5
r8

Describe Owen’s error.

Answer 1

Owen treated s^{-5} as s^5 instead of as a reciprocal. The rule is a^{-n} = 1/a^n, so

r^{-8}s^{-5} = (1/r^8)(1/s^5) = 1/(r^8 s^5).

Owen’s step 1/r^8 ⋅ s^5 = s^5/r^8 is wrong because s^{-5} ≠ s^5.