How do we simplify expressions with rational exponents?

Rational exponents are fractions, for example like this:

The numerator is the number of times the base is to be multiplied. The denominator is the root being taken.
You'll know your expression is simplified when:

1. The exponent isn't negative: You must flip the exponent and put it in the denominator and make it positive.
2. When the index are really simplified: if you can simplify the fraction exponent, do it! Its much easier!

Lets try a Problem:

Here 27 is raised to the 2/3rd power. The denominator is the root, so 27 to the cube root is 3. Than you square 3 and your final answer is 9. Viola! Simple as that.

Now Try this problem on your own:
What is 25/9 to the 1/2 Power?






Sources:

• http://www.solving-math-problems.com/image-files/math_rad_frac_exp.png
• https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcQ5GY6vvbHS0glig6_EY2DjtvWd45kOcuOvBBgbKuY9xhD06OR9
• http://www.mathops.com/free/a1rr010.php