Raising numerical inequalities to a power
Answers are for parents and teachers.
1
Compare (3/5)³ and (4/5)³.
(3/5)³ < (4/5)³
2
Compare √5 and ³√11 (raise to the 6th power).
√5 > ³√11, because 125 > 121
3
Compare 9^(-1/3) and 8^(-1/3).
9^(-1/3) < 8^(-1/3)
4
If a > b > 0, compare a^(1/2) and b^(1/2).
a^(1/2) > b^(1/2)
5
To compare 2⁵⁰ and 3³⁰, what power helps? Which is greater?
Take 10th roots: 2⁵ = 32 and 3³ = 27, so 2⁵⁰ > 3³⁰.