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 5-7 Rational Exponents

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: 1) NO negative exponents 2) NO fractional exponents in the denominator 3) NOT a complex fraction 4) The index of any remaining radical is the least number possible.

Two different ways to simplify expressions with rational exponents: Method 1: - rewrite the expression - then simplify Method 2: - rewrite the base in exponential form 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)