# How do you simplify root7( x^9)/root5(x^6)?

Apr 28, 2016

First change the roots to indices with fractions.
Use the law of indices for dividing indices with the same bases by subtracting the indices.

#### Explanation:

x^(9/7) ÷ x^(6/5)

= ${x}^{\frac{9}{7} - \frac{6}{5}}$
(remember to find the LCD)

= ${x}^{\frac{45 - 42}{35}}$

= ${x}^{\frac{3}{35}}$