5.7 Rational Exponents

1. 5.7 � Rational Exponents Basic concept Converting from rational exponent to radical form Evaluating expressions with rational exponents Simplifying

2. Writing radicals in exponential form Note that (vx)2 = x = x1 Is there a way for us to represent vx using exponents? Suppose we call the power equivalent to a square root �z� Then (vx)2 = (xz)2 = x = x1 By the third law of exponents, (xz)2 = x2z Since x2z = x1, 2z = 1 and z = � Therefore x1/2 is equivalent to vx

3. More on rational exponents By similar reasoning, 3v2 is equivalent to 21/3 4v5xy is equivalent to (5xy)1/4 What about something like 5vx3? This is the 5th root of x cubed To write using rational exponents, the index goes in the denominator, and the power goes in the numerator Thus, 5vx3 = x 3/5 Similarly, v28 = 28/2 = 24 = 16 Note from the above example that rational exponents may be reduced like any other fraction

4. Example 7-1a