How do you simplify # x^(2/3)(x^(1/4) - x) #?

1 Answer

Answer:

#x^(11/12)-x^(5/3)#

Explanation:

We can distribute the #x^(2/3)# term across the bracketed terms:

#x^(2/3)(x^(1/4)-x)#

#x^(2/3)xxx^(1/4)-x^(2/3)xxx#

Let's first note that #x=x^1#

#x^(2/3)xxx^(1/4)-x^(2/3)xxx^1#

Let's also remember that when multiplying numbers with the same base, we add exponents, i.e. #x^a xx x^b = x^(a+b)#:

#x^(2/3+1/4)-x^(2/3+1)#

And now we combine fractions the way we always do (i.e. make the denominators the same)

#x^(2/3(4/4)+1/4(3/3))-x^(2/3+1(3/3))#

#x^(8/12+3/12)-x^(2/3+3/3)#

#x^(11/12)-x^(5/3)#