1. Exponents & Radicals – Rules for Exponents Variable – a letter used to represent an unknown quantity or value x, y, a, b, m, n, etc. Coefficient – the number that appears in front of a variable 2a, - 3d, 5x, -9y, etc Exponent – usually a number that appears as a superscript for a variable or base ( constant ). Sometimes referred to as “raising to a power “. a 2, b 3, 5 2, -10 4 There are specific rules when dealing with variables / bases and their exponents. These rules are designed to make it easier to multiply or divide variables that have large exponents. ALSO, because we are now using the letter “x” to represent something, we will no longer show multiplication as 2 x 3… from here forward, multiplication will be shown as a dot … Means 2 times 3

2. Exponents & Radicals – Rules for Exponents AND, when nothing appears between numbers and letters, or two or more letters, multiplication is implied…

3. Exponents & Radicals – Rules for Exponents Example #1 :

4. Exponents & Radicals – Rules for Exponents Example #1 : Example # 2 :

5. Exponents & Radicals – Rules for Exponents Example #1 : Example # 2 : Example # 3 :

6. Exponents & Radicals – Rules for Exponents Example #1 : Example # 2 : Example # 3 : Example # 4 :

7. Exponents & Radicals – Rules for Exponents Example #1 : Example # 2 : Example # 3 : Example # 4 : When you think about it, it is not practical to write x 13 as thirteen individual x’s… So some general rules were developed. I would write them down !!!

8. Exponents & Radicals – Rules for Exponents RULES FOR EXPONENTS

9. Exponents & Radicals – Rules for Exponents RULES FOR EXPONENTS - When multiplying like variables, ADD your exponents

10. Exponents & Radicals – Rules for Exponents RULES FOR EXPONENTS - When multiplying like variables, ADD your exponents - When dividing like variables, SUBTRACT your exponents

11. Exponents & Radicals – Rules for Exponents RULES FOR EXPONENTS - When multiplying like variables, ADD your exponents - When dividing like variables, SUBTRACT your exponents - When a variable has an exponent, AND is again raised to another exponent, multiply exponents

12. Exponents & Radicals – Rules for Exponents RULES FOR EXPONENTS - When multiplying like variables, ADD your exponents - When dividing like variables, SUBTRACT your exponents - When a variable has an exponent, AND is again raised to another exponent, multiply exponents - When a variable has a negative exponent, the variable is moved to the denominator and the exponent becomes positive.

13. Exponents & Radicals – Rules for Exponents RULES FOR EXPONENTS - When dividing like variables, SUBTRACT your exponents - When a variable has an exponent, AND is again raised to another exponent, multiply exponents - When a variable has a negative exponent, the variable is moved to the denominator and the exponent becomes positive.

14. Exponents & Radicals – Rules for Exponents RULES FOR EXPONENTS - When a variable has an exponent, AND is again raised to another exponent, multiply exponents - When a variable has a negative exponent, the variable is moved to the denominator and the exponent becomes positive.

15. Exponents & Radicals – Rules for Exponents RULES FOR EXPONENTS - When a variable has a negative exponent, the variable is moved to the denominator and the exponent becomes positive.

16. Exponents & Radicals – Rules for Exponents RULES FOR EXPONENTS

17. Exponents & Radicals – Rules for Exponents Try some for yourself…don’t move forward until you’ve tried each example; then see hit the space bar to see the answer.

18. Exponents & Radicals – Rules for Exponents Try some for yourself…don’t move forward until you’ve tried each example; then see hit the space bar to see the answer.

19. Exponents & Radicals – Rules for Exponents Try some for yourself…don’t move forward until you’ve tried each example; then see hit the space bar to see the answer.

20. Exponents & Radicals – Rules for Exponents Try some for yourself…don’t move forward until you’ve tried each example; then see hit the space bar to see the answer. If a variable or number has no exponent, it is assumed to be a one. Also, I placed the 1 in my answer along with “y”, but I could have omitted it.

21. Exponents & Radicals – Rules for Exponents Try some for yourself…don’t move forward until you’ve tried each example; then see hit the space bar to see the answer.

22. Exponents & Radicals – Rules for Exponents Try some for yourself…don’t move forward until you’ve tried each example; then see hit the space bar to see the answer.

23. Exponents & Radicals – Rules for Exponents Try some for yourself…don’t move forward until you’ve tried each example; then see hit the space bar to see the answer.

24. Exponents & Radicals – Rules for Exponents Try some for yourself…don’t move forward until you’ve tried each example; then see hit the space bar to see the answer.

25. Exponents & Radicals – Rules for Exponents Try some for yourself…don’t move forward until you’ve tried each example; then see hit the space bar to see the answer.

26. Exponents & Radicals – Rules for Exponents Try some for yourself…don’t move forward until you’ve tried each example; then see hit the space bar to see the answer.

27. Exponents & Radicals – Rules for Exponents Try some for yourself…don’t move forward until you’ve tried each example; then see hit the space bar to see the answer.

28. Exponents & Radicals – Rules for Exponents Try some for yourself…don’t move forward until you’ve tried each example; then see hit the space bar to see the answer.