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

Jul 4, 2016

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

#### Explanation:

Follow the normal method of the distributive law, but there are indices to consider as well.

If the bases are the same, then add the indices when multiplying.

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

${x}^{\frac{11}{12}} - {x}^{\frac{5}{3}} \text{ } \frac{8 + 3}{12} = \frac{11}{12}$

One might consider taking out a common factor of ${x}^{\frac{11}{12}}$
but this would not produce an answer that can be simplified further anyway.