Solve for x equation x^6-64=0?

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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You need to solve the given equation, hence, you need to isolate the term that contains the variable `x^6` to the left side, adding `64` both sides, such that:

`x^6 = 64`

You need to exponentiate both sides by `(1/6)` , such that:

`(x^6)^(1/6) = 64^(1/6)`

Using the following law of exponents, yields:

`x^(6*(1/6)) = 64^(1/6)`

Since you may express `64` as `2^6` , yields:

`x^(6*(1/6)) = 2^(6*(1/6))`

Reducing duplicate factors yields:

`x = 2`

Hence, evaluating the solution to the given equation, using the laws of exponents, yields `x = 2` .

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aruv | High School Teacher | (Level 2) Valedictorian

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Here  is problem  to solve the equation  `x^6=64`

`(A^m)^(1/m)=A`

`and`

`((-A)^m)^(1/m)=-A`  if m is an even integer.

Thus `((A)^m)^(1/m)=+-A`

`(x^6)^(1/6)=((+-2)^6)^(1/6)`

`x=+-2`

Let define function `f(x)=x^6-64 ` , draw its graph and observe where it meet x-axis

So graph meets x ais at x=-2,2

i.e. 2,-2 are zeros of f(x) or roots of equation f(x)=0.

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