I will do the second, you do the others in the same way.
(x - 12)^3/2 = 64 , raise both sides to the 2/3, (notice the reciprocal of 3/2)
[(x - 12)^3/2]^(2/3) = 64^(2/3)
x-12 = 16
x = 28
solve
1:
n^3/2 = 125
2:
(x - 12)^3/2 = 64
3:
3125 = (-1-18t)^5/3
2 answers
1. n^(3/2) = 125.
Take cube root of both sides(raise to 1/3 power):
n^(1/2) = 5,
Sqrt(n) = 5,
Square both sides:
n = 25.
check: 25^(3/2) = 25 * 25^(1/2) = 25 * sqrt(25) = 25 * 5 = 125.
Take cube root of both sides(raise to 1/3 power):
n^(1/2) = 5,
Sqrt(n) = 5,
Square both sides:
n = 25.
check: 25^(3/2) = 25 * 25^(1/2) = 25 * sqrt(25) = 25 * 5 = 125.
1 answer