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

${x}^{\frac{11}{12}} - {x}^{\frac{5}{3}}$

#### Explanation:

We have:

${x}^{\frac{2}{3}} \left({x}^{\frac{1}{4}} - x\right)$

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

${x}^{\frac{2}{3}} \left({x}^{\frac{1}{4}} - {x}^{1}\right)$

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Before we move on, it's important to see that $\left({x}^{\frac{1}{4}} - {x}^{1}\right) \ne {x}^{- \frac{3}{4}}$

For instance, if we set $x = 16 \implies \left({16}^{\frac{1}{4}} - {16}^{1}\right) \ne {16}^{- \frac{3}{4}} \implies \left(2 - 16\right) \ne - \frac{1}{8}$

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We can use the rule ${x}^{a} \times {x}^{b} = {x}^{a + b}$:

${x}^{\frac{2}{3}} \left({x}^{\frac{1}{4}} - {x}^{1}\right)$

${x}^{\frac{1}{4} + \frac{2}{3}} - {x}^{1 + \frac{2}{3}}$

${x}^{\frac{3}{12} + \frac{8}{12}} - {x}^{\frac{3}{3} + \frac{2}{3}}$

${x}^{\frac{11}{12}} - {x}^{\frac{5}{3}}$