Question

How do you solve `2(x+4)^(2/3) = 8`?

Answer 1

Note that `q^(2/3) = (q^2)^(1/3)`

So
`2(x+4)^(2/3) = 8`

can be evaluated as
`2(x^2+8x+16)^(1/3) = 8`

cube both sides giving:
`8 (x^2+8x+16) = 8xx8xx8`
or
`x^2+8x+16 = 64`
`rarr`
`x^2+8x-48=0`

factoring:
`(x+12)(x-4) = 0`

So
`x=-12`
or
`x=4`