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

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

#### Explanation:

We can distribute the ${x}^{\frac{2}{3}}$ term across the bracketed terms:

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

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

Let's first note that $x = {x}^{1}$

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

Let's also remember that when multiplying numbers with the same base, we add exponents, i.e. ${x}^{a} \times {x}^{b} = {x}^{a + b}$:

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

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

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

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

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