Wednesday, 12 May 2010
EXPONENTS AND RADICALS
1. Multiplying and Dividing Powers
To multiply powers with the same base, add the exponents and keep the same base:
3 4 3+4 7
b X b = b = b
To divide powers with the same base, subtract the exponents and keep the same base:
12 8 12-8 4
b / b = b = b
2. Raising Powers to Powers
To raise a power to a power, multiply the exponents:
3 5 3x5 15
(x ) = x = x
3. Negative Powers
A number raised to a negative exponent is simply the reciprocal of that number raised to the corresponding positive exponent.
-3
2 = 1 = 1
3 8
2
4. Simplifying Square Roots ________
V
To simplify a square root, factor out the perfect squares under the radical, unsquare them and put the result in front:
__ ____ __ __ ___
V12 = V 4X3 = V 4 X V 3 = 2 V 3
5. Adding and Subtracting Roots
You can add or subtract radical expressions when the part under the radicals is the same:
__ __ ___
2 V7 + 3 V7 = 5 V7
Don't try to add or subtract when the radicals are different. You cannot simplify expressions like: ___ __
2 V 3 + 3 V 5
6. Multiplying and Dividing Roots
The product of square roots is equal to the square root of the product:
__ __ ______ ___
V 2 x V 3 = V 2 X 3 = V 6
The quotient of square roots is equal to the square root of the quotient:
__ ___ ____ ___
V 8 / V 2 = V 8/4 = V 2
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