Question

How do you solve for x in `3(x-6)^(5/2) = 96`?

Answer 1

`3(x-6)^(5/2)=96`

Reduce by removing obvious common factor (`3`)
`rarr (x-6)^(5/2)=32`

Note that `32 =2^5` so we can take the 5th root of both sides
`rarr (x-6)^(1/2) = 2`

Square both sides to clear the root on the left side
`rarr x-6 = 4`

Isolate `x`
`rarr x=10`