No.
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8^3 = 512
if it is to the 2nd power it is 64 if it is to the 3rd power it is 512 .
8^4 = 4096.
Such that 83 = 8 x 8 x 8 = 512, 8-3 = 1/8 x 1/8 x 1/8 = 1/512
512^(1/3) = (2^9)^(1/3) = 2^(9×1/3) = 2^3 = 8. The cube root of 512 is 8.