5-7 Rational Exponents Objectives Students will be able to: Write expressions with rational exponents in radical form, and vice versa Simplify expressions in exponential or radical form

When a term contains a rational exponent (fraction), the term can be rewritten in radical form. The denominator of the fraction is the index. The numerator of the fraction is the exponent to which the radicand is raised. The reverse is also true. A radical expression can be rewritten using rational exponents.

Example 1: Write each expression in radical form. 1) 2) 3) Try these

Example 2: Write each radical using rational exponents. 1) 2) Try 3)

When simplifying expressions with rational exponents, there are certain conditions that must be met.

As with anything, pick the method you like best and use that. Generally, there are two different ways to simplify expressions with rational exponents. Method 1 involves rewriting the expression (as we had in the previous exercise) and then simplifying. Method 2 involves rewriting the base in exponential form, and then simplifying. As with anything, pick the method you like best and use that.

Here is the general definition of rational exponents. It’s finally time to jump into more examples…

Example 3: Evaluate each expression. 1) 2) 3)

Try these. 4) 5) 6)

Example 4: Simplify each expression. 1) 2) Try these. 3) 4)

5) 6)

7) 8) 9)

Try these. 10) 11) 12) 13)