Solve for X.

X^3=27
x = 3

because 3 * 3 = 9
and 9 * 3 = 27. Correct?

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[x]= 16
X = 4^3

because 4 * 2 = 8
and 8 * 2 = 16. Correct?

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(x-2)^4=16

I need help on this one!

x^3 = 27

Take cube root of both sides
x = 3

Because, 3 * 3 * 3 = 27

I'm not sure what your 2nd problem is.
Is your problem, x^4 = 16 ?
If so,
x^4 = 16
Take the forth root of both sides
x = +- 2

Because, 2 * 2 * 2 * 2 = 16
Or, -2 * -2 * -2 * -2 = 16

FYI, 4^3 = 4 * 4 * 4 = 64

(x - 2)^4 = 16
Take the forth root of both sides
+- (x - 2) = 2
x - 2 = 2
x = 4

-x + 2 = 2
x = 0