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put this solution on YOUR website! It is very good that you typed the expression corectly and clearly .
On way
(x+1)^(-3/2)=8
[(x+1)^(-1/2)]3 = 2^3,
So, (x+1)^(-1/2) = 2.
Square on both sides:
(x+1)^(-1) = 4,
Or 1/(x+1) = 4,
So, (x+1) = 1/4,
x = -3/4.
Another way:
Square on both sides:
(x+1)^(-3) = 8^2 = 64 = 2^6,
Take cubic root on both sides:
(x+1)^(-1) = (2^6)^(1/3) = 2^2 =4,
So, x+1 = 1/4, x = -3/4
Check (-3/4 + 1)^(-3/2) = (1/4)^(-3/2) = (1/2)^2*(-3/2)
= (1/2)^(-3) = [(1/2)^(-1)]^3
= 2^3 = 8 (correct)
Kenny
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