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MCF3M1 Date: ____________ Lesson 3 - Working with Rational Exponents Rational Number: a number that can be expressed as the ratio of two integers, where the divisor is not zero A. In general: a 1 n n a , for a 0 n (where n is a natural number) a is called a radical and means the nth root of a We can write an expression in exponential form or radical form: 2 1 5 5 Exponential Form B. Recall power to a power rule : 2 Radical Form a (a ) (a ) xy x y y x This will help us with the more complicated radical exponents , where m and n are natural numbers Examples: 1. Write in radical form and solve: a) x 1 3 b) 49 1 2 1 c) 64 3 MCF3M1 1 1 d) 27 3 g) 4 1 e) y 2 f) (2 x) 4 3 2 2. Write using exponential form: a) 101 b) 5 c) 10 3 10 5 3. Evaluate: 4 1 b) 8 3 a) (8) 3 c) (8 x ) 6 2 3 Page 2 MCF3M1 Rule Example Page 3