Here the equation is `x^(2/3)=1/16` .

Taking cube of both sides we get

`(x^(2/3))^3=(1/16)^3`

or, `(x)^((2/3).3)=(1/16)^3`

or, `(x)^2=((1/4)^2)^3`

or, `(x)^2=(1/4)^6`

`` or, `(x)^2=((1/4)^3)^2`

or, `x^2-((1/4)^3)^2=0`

or, `(x-(1/4)^3)(x+(1/4)^3)=0`

So, `(x-(1/4)^3)=0` and `(x+(1/4)^3)=0`

so, `x=(1/4)^3` or `x=-(1/4)^3`

So, `x=1/64` 0r `x=-1/64` .

Try to get rid of the exponent 2/3 on left side. To do that, we raised both sides by the reciprocal of 2/3 which is 3/2.

`(x^(2/3))^(3/2) = (1/16)^(3/2)`

`x = (1/16)^(3/2)`

Take note that 3/2 = 1/2 * 3.

`x = ((1/16)^(1/2))^(3) = (1/4)^3`

The exponent indicate how many times we multiply the base by itself.

`x = (1/4)^3 = (1/4)*(1/4)*(1/4) = 1/64`

Hence, **x = 1/64**.

`x^(2/3)=(1/16)`

`x^(2/3)=(1/4^2)`

`x^(2/3)=(1/4)^2`

`(x^(1/3))^2=(1/4)^2`

`(x^(1/3))^2-(1/4)^2=0`

Factorise the equation by formula `a^2-b^2=(a-b)(a+b)` ,so we have

`(x^(1/3)-1/4)(x^(1/3)+1/4)=0`

`x^(1/3)-1/4=0`

`x^(1/3)=1/4`

`(x^(1/3))^3=(1/4)^3`

`x=1/64`

or

`x^(1/3)+1/4=0`

`x^(1/3)=-1/4`

`(x^(1/3))^3=(-1/4)^3`

`x=-1/64`

`` Thus

`x=+-1/64`