Question 1145610
x^(3/4) = 6 can be solved as follows:


raise both sides of the equation to the power of (4/3) to get:
x^(3/4)^(4/3) = 6^(4/3)
this is equivalent to:
x^(3/4 * 4/3) = 6^(4/3)
simplify to get x= 6^(4/3) = 10.90272356
confirm by replacing x with that to get:
10.90272356^(3/4) = 6
result is 6 = 6, confirming the solution is correct.


x^(3/4) is the same as the fourth foot of x^3 and is also the same as the fourth root of x raised to the third power.


this looks like (x^3)^(1/4) or (x^(1/4))^3


the basic rule for exponent arithmatic is:


(x^a)^b = x^(a*b)
if a is 3 and b is (1/4), you get (x^3)^(1/4) = x^(3*1/4) = x^(3/4)
if a is 1/4 and b is 3, you get (x^(1/4)^3 = x^((1/4)*3) = x^(3/4)