1. Rules of Exponents and Scientific Notation
5.6
Rules of Exponents and Scientific Notation

2. Exponents
When a number is written with an exponent, there are two parts to the expression: baseexponent
The exponent tells how many times the base should be multiplied together.

3. Product Rule Simplify: 34 • 39 34 • 39 = 34 + 9 = 313
64 • 65 = = 69

4. Quotient Rule
Simplify:
Simplify:

5. Zero Exponent Rule Simplify: (3y)0 (3y)0 = 1 Simplify: 3y0
= 3(1) = 3

6. Negative Exponent Rule
Simplify: 64

7. Power Rule Simplify: (32)3 (32)3 = 32•3 = 36 Simplify: (23)5
(23)5 = 23•5 = 215

8. Scientific Notation
Many scientific problems deal with very large or very small numbers.
93,000,000,000,000 is a very large number.
is a very small number.

9. Scientific Notation continued
Scientific notation is a shorthand method used to write these numbers.
9.3  and 4.82  10–10 are two examples of numbers in scientific notation.

10. To Write a Number in Scientific Notation
1. Move the decimal point in the original number to the right or left until you obtain a number greater than or equal to 1 and less than 10.
2. Count the number of places you have moved the decimal point to obtain the number in step 1.
If the decimal point was moved to the left, the count is to be considered positive. If the decimal point was moved to the right, the count is to be considered negative.
3. Multiply the number obtained in step 1 by 10 raised to the count found in step 2. (The count found in step 2 is the exponent on the base 10.)

11. Example Write each number in scientific notation. a) 1,265,000,000.
1.265  109 b)
4.32  1010

12. To Change a Number in Scientific Notation to Decimal Notation
1. Observe the exponent on the 10. 2.
a) If the exponent is positive, move the decimal point in the number to the right the same number of places as the exponent. Adding zeros to the number might be necessary.
b) If the exponent is negative, move the decimal point in the number to the left the same number of places as the exponent. Adding zeros might be necessary.

13. Example Write each number in decimal notation. a) 4.67  105 467,000

16. Homework
P. 266 # 13 – 95 eoo