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

1 Answer
MathFact-orials.blogspot.com
Jun 1, 2017

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)

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