How do you find the zeroes of $f (x) = x^{6} - 64$ $f (x) =x^6 − 64$ ?

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Answer 1 · 2015-07-02T13:39:51

First note that $64 = 2^{6}$ $64=2^6$

Since the exponent is even, $64 = {(- 2)}^{6}$ $64=(-2)^6$ also

You can now say that $x^{6} = 2^{6} or x^{6} = {(- 2)}^{6}$ $x^6=2^6orx^6=(-2)^6$

In other words: $x = 2 or x = - 2$ $x=2orx=-2$

How do you find the zeroes of f (x) =x^6 − 64f(x)=x6−64f (x) =x^6 − 64?