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
2 answers
(x^6)^(1/24) = x^(1/4)
{(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
[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
1 answer