1. Laws of Exponents Objective: TSW simplify powers. TSW simplify radicals. TSW develop a vocabulary associated with exponents. TSW use the laws of exponents to simplify.

2. Exponents The lower number is called the base and the upper number is called the exponent. The exponent tells how many times to multiply the base.

3. Exponents 7 3 exponent base power

4. 1. Evaluate the following exponential expressions: A. 4 2 = 4 x 4 = 16 B. 3 4 = 3 x 3 x 3 x 3 = 81 C. 2 3 = D. (-1) = 7

5. Squares To square a number, just multiply it by itself. = = 3 x 3 = 93 squared =

6. Perfect Squares 1² = 1 2² = 4 3² = 9 4² = 16 5² = 25 6² = 36 7² = 49 8² = 64 9² = 81 10² = 100 11² = 121 12² = 144 13² = 169

7. Square Roots A square root goes the other direction. 3 squared is 9, so the square root of 9 is 3 3 9

8. Square Roots

9. Radicals - The inverse operation of raising a number to a power. For Example, if we use 2 as a factor with a power of 4, then we get 16. We can reverse this by finding the fourth root of 16 which is 2. = 2 16 4

10. Radicals In this problem, the 16 is called the radicand, the 4 is the index, and the 2 is the root. The symbol is known as the radical sign. If the index is not written, then it is understood to be 2. The entire expression is known as a radical expression or just a radical.

11. Example Simplify: a)c) b)d) 81 27 16 8 3 4 3

12. Laws of Exponents Whenever we have variables which contain exponents and have equal bases, we can do certain mathematical operations to them. Those operations are called the “Laws of Exponents.”

13. Laws of Exponents

15. Zero Exponents A nonzero based raise to a zero exponent is equal to one a 0 = 1

16. Negative Exponents a -n = ( 1 ______ a n ) A nonzero base raised to a negative exponent is the reciprocal of the base raised to the positive exponent.

17. Basic Examples

20. Examples 1. 2. 3. 4.