How do you simplify $\frac{\sqrt[7]{x^{9}}}{\sqrt[5]{x^{6}}}$ $root7( x^9)/root5(x^6)$ ?

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Answer 1 · 2016-04-28T21:55:20

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

$x^{\frac{9}{7}} \div x^{\frac{6}{5}}$ $x^(9/7) ÷ x^(6/5)$

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

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

= $x^{\frac{3}{35}}$ $x^(3/35)$

How do you simplify 7√x95√x6root7( x^9)/root5(x^6)?