Question

a student starts with a positive number, x^6, and take the square root three times and the cube root once. this is equivalent to which of the following?

a. x^1/4

b. x^4/3

c. x^3/4

d. x^4

Answer 1

(x^6)^(1/24) = x^(1/4)

Answer 2

{(x^6)^[(1/2)^3]}^(1/3)

[x^(6/8)]^(1/3)

x^(2/8)

x^1/4

check with x = 2
2^6 = 64
sqrt = 8
sqrt = 2sqrt 2
sqrt = sqrt 2 sqrt (sqrt 2)
= sqrt ( (sqrt2)^3)
now take the cube root of that
[sqrt (2 ^3/2)]^1/3
sqrt (2^1/2) = 2^1/4 sure enough