Fractional exponents

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1. FRACTIONAL EXPONENTS

2. Let’s Learn The laws of exponents for integral exponents are applicable also for fractional or rational exponents. Study the following examples . Example 1. Simplify using the laws of exponents. Express the answer using positive exponents only.

3. a · a = 2. = a · a = a + = a = a 1 = a = a - = a

4. 3. = 4. 3 = = 4 2 a 2 = 16a = 16a 3 = x = x

5. Example 2. Evaluate .   Steps Solution 1. Express the base in exponential form. (27 = 3 3 ) = 2. Use the power of a power law of exponents. = or = = 3 2 = 9 3. Simplify the result by applying the laws of exponents. So, = 9 Steps Solution 1. Express the base in exponential form. (27 = 3 3 ) 2. Use the power of a power law of exponents. 3. Simplify the result by applying the laws of exponents.

6. Example 3. Evaluate   Steps Solution 1. Express the base in exponential form. (32 = 2 5 ) = 2. Use the power of a power law of exponents. = or = 2 4 = 16 3. Simplify the result by applying the laws of exponents. So, = 16 Steps Solution 1. Express the base in exponential form. (32 = 2 5 ) 2. Use the power of a power law of exponents. 3. Simplify the result by applying the laws of exponents.

7. Example 4. Evaluate (   Steps Solution 1. Express the base in exponential form. (81 = 3 4 ) ( = 2. Use the power of a power law of exponents. = or = 3 5 = 243 3. Simplify the result by applying the laws of exponents. So, ( = 243 Steps Solution 1. Express the base in exponential form. (81 = 3 4 ) 2. Use the power of a power law of exponents. 3. Simplify the result by applying the laws of exponents.

8. Example 5. Evaluate   Steps Solution 1. Express the base in exponential form. (-32 = -2 5 ) = 2. Use the power of a power law of exponents. = or = -2 3 = -8 3. Simplify the result by applying the laws of exponents. So, = -8 Steps Solution 1. Express the base in exponential form. (-32 = -2 5 ) 2. Use the power of a power law of exponents. 3. Simplify the result by applying the laws of exponents.

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