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