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The cube root of 4 to the power of 3 is the same as the cube root of 64, which equals 4. This is because raising a number to the power of 3 and then taking the cube root of that result cancels out the exponentiation. In this case, 4 cubed is 64, and the cube root of 64 is 4.
82/3 would be the cubed root of the square of the number 8 or (82)1/3. In other words, 8 squared is 64. So you want the cubed root of 64, which is 4.
That simply means that there is both a positive and a negative number which, when squared, gives you 64.
Since 8x8 = 64 and (-8)x(-8) is also = 64
They are cubed values. 1 cubed is 1, 2 cubed is 8, 3 cubed is 27, 4 cubed is 64, 5 cubed is 125 and 6 cubed is 216.