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

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Answer 1 · 2017-02-01T08:31:16

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

We have:

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

I'm first going to rewrite this so that we can see the exponent on the "plain" $x$ term: $x=x^1 =>$

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

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Before we move on, it's important to see that $(x^(1/4)-x^1)!=x^(-3/4)$

For instance, if we set $x=16 => (16^(1/4)-16^1)!=16^(-3/4)=>(2-16)!=-1/8$

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We can use the rule $x^a xx x^b=x^(a+b)$ :

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

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

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

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

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