Let's first combine the number terms on the left and the #x# term on the right:
#26=-1+(27x)^(3/4)#
#27=(27x)^(3/4)#
And now for the pesky #3/4# thing... first off, the numerator of the fraction is the number of times the term is cubed. The denominator is the nth root - in this case the 4th root. So for us to get rid of the pesky exponent, we're going to take the inverse and make the fraction one (and of course we'll do that to the other side as well). Like this:
Let's first just take the #(27x)^(3/4)#. The inverse of the #3/4# is #4/3# and if we do it, we get:
#((27x)^(3/4))^(4/3)=(27x)^(3/4xx4/3)=(27x)^(12/12)=(27x)^1=27x#
Ok - so now let's take the #4/3# power to both sides:
#27^(4/3)=((27x)^(3/4))^(4/3)=27x#
So what does #27^(4/3)# equal? Let's first see that #27=3^3# and so we can take the cube root of 27 and get 3. And if we then take 3 to the 4th power, it's 81 (#3xx3xx3xx3=9xx9=81#). So we have:
#27^(4/3)=81=27x#
#x=81/27=3#
