EXPONENTS AND RADICALS

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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         3×5              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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