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

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SUMMARY

The equation (16-x²)³/2 = 40 can be solved by first rewriting it as (16-x²)^(3/2) = 40. To simplify, raise both sides to the power of 2/3, resulting in 16 - x² = 40^(2/3). This allows for straightforward calculation of x. The initial misunderstanding involved incorrectly stating that a square root was taken, when in fact, the exponent was simply rewritten.

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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
 
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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).
 
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.
 

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