Question 574509
Let's first simplify it a bit. I cannot get those exponents to show properly, but you know what I mean.
{{{3(x+1)^(4/3)= 48}}} --> {{{3(x+1)^(4/3)/3 = 48/3}}} --> {{{(x+1)^(4/3) = 16}}}
The rest gets a little more creative, using properties of exponents. (Note that I got creative writing {{{(3/4)}}} as 0.75 at one point. I did it to avoid the problem with the tops of exponents being chopped off).
{{{(x+1)^(4/3) = 16}}} --> {{{((x+1)^(4/3))^(3/4) = 16^(3/4)}}} --> {{{(x+1)^((4/3)*(3/4))=(2^4)^(3/4)}}} --> {{{(x+1)^1=2^((4*0.75))}}} --> {{{x+1=2^3}}} --> {{{x+1=8}}} --> {{{highlight(x=7)}}}