How Do You Solve (16-x²)³/2 = 40 for x?

[angel]

hi,
im trying to solve this for x:

(16-x^2)^3/2 = 40

ive simplified it by taking the square root, so i get:

sqrt(16-x^2)^3) = 40

now i square both sides and i get:

(16-x^2)^3 = 1600 (Not sure if this is right)

im not sure what to do next. i think i can take the cube root of both sides, but I am not sure.
Can someone please help me.
thanks

 

[Muzza]

Yes, you take the cube root of both sides. In fact, you could've just raised both sides to the power of 1/(3/2) = 2/3 in the first place, to get 16 - x^2 = 40^(2/3) (which should be easy to solve).

 

[HallsofIvy]

By the way, you didn't actually "take the square root" at the beginning: you simply rewrote the "1/2" power as a square root. You could have said "square both sides" initially.