The two laws of exponents are
For any real number a and any rational exponents m and n:
1. In multiplying, we can add exponents if the bases are the same. 2. In dividing, we can subtract exponents if the bases are the same. 3. To raise a power to a power, we can multiply the exponents. 4. To raise a product to a power, we can raise each factor to the power. 5. To raise a quotient to a power, we can raise both the numerator and the denominator to the power.
SIMPLIFYING RADICAL EXPRESSIONS
1. Convert radical expressions to exponential expressions.
2. Use arithmetic and the laws of exponents to simplify.
3. Convert back to radical notation when appropriate.
Important: This procedure works only when all expressions under radicals are nonnegative since rational exponents are not defined otherwise. With this assumption, no absolute-value signs will be needed.
Here are some example of it. EXAMPLES Use the laws of exponents to simplify. 16. 3 1/5 _ 33/5 _ 31/5_3/5 _ 34/5 Adding exponents
17. 71/4 / 71/2 _ 71/4_1/2 _ 71/4_2/4 _ 7_1/4 _1 71/4 Subtracting exponents 18. _7.22/3_3/4 _ 7.22/3 _ 3/4 _ 7.26/12 _ 7.21/2 Multiplying exponents 19. _ a_1/6b1/5 _b1/5a1/6 _a_1/3b2/5_1/2 _ a_1/3 _ 1/2 _ b2/5 _ ½ Raising a product to a power and multiplying exponents The rational exponents can be used to simplify some radical expressions. Example: _3 5 _ _2