Answer:
x = 27
Step-by-step explanation:
Given the expression [tex]{2x^{\frac{5}{3} }-22 = 464[/tex], we are to find the value of x in the expression. This is as shown below;
[tex]{2x^{\frac{5}{3} }-22 = 464[/tex]
add 22 to both sides
[tex]{2x^{\frac{5}{3} }-22 = 464+22\\\\[/tex]
[tex]{2x^{5/3} =486[/tex]
divide both sides by 2
[tex]\frac{2x^{5/3}}{2} =\frac{486}{2}\\ x^{5/3} = 243[/tex]
raise both sides to the power of 3/5
[tex](x^{5/3})^{3/5} = (243)^{3/5}\\x = (\sqrt[5]{243}) ^3\\x = 3^3\\x = 27[/tex]
Hence the value of x is 27
