2. 3 3 4 4 3 3 4 4 = = 3 3 x 3x 3 x 3x 3 x 3x 3 x 3x 3 x 3x 3 x 3x 3

3. = = 3 3 x 3 Too many buttons! AND… what if it is something like 0.1279 25 ? xyxy yxyx ^ 3 3 4 4 = = 81

4. Communicate Your Understanding MHR 113:C1, C2, C3, C4

5. Are these the same thing? -3 2 (-3) 2 =-(3x3) =-9 =(-3)(-3) =9

6. Page 120 #6 PRODUCTExpanded FormSingle Power 3 2 x 3 4 4 3 x 4 3 6 4 x 6 1 2 4 x 2 2 x 2 3 k 3 x k 5 Own example (-2) 3 x (-2) 3

7. #9. Reflect: How can you write a product of powers using a single power? Complete: #7, #8 #10. Write a rule for finding the product of powers. x a x x b = x a+b PRODUCT RULE x SHORTCUT Ensure same base! Add the exponents.

8. Apply the Product Rule (x shortcut) a) b) c) Apply the product rule to write each as a single power. Evaluate the expression given in c)

9. Page 120 #11 QuotientExpanded FormSingle Power 55  5355  53 7 4  7 1 10 6  10 4 2 7  2 6 p 8  p 5 Own example (-2) 5 x (-2) 2

10. #14. Reflect: How can you write a quotient of powers using a single power? Complete: #12, 13 #15. Write a rule for finding the quotient of powers. x a  x b = x a-b QUOTIENT RULE  SHORTCUT Ensure same base! Subtract the exponents.

11. Apply the Quotient Rule (  shortcut) a) b) c) Apply the quotient rule to write each as a single power. Evaluate the expression given in b) and c)

12. Page 123 #1, 2, 3 Power of a Power Expanded Form Single Power (2 2)3 (5 3)4 (10 4)2

13. #4. Write a rule for finding the power of a power. (x a ) b = x a x b POWER OF A POWER SHORTCUT Multiply the exponents for each base in the brackets

14. ExampleExpandedSimplifiedExponent Rule Multiplication Division Power of Power Law Power of a Product Power of a Quotient

15. The bases must be the same!

16. Can you simplify this?

17. MHR textbook p114 #5, #6, #8 p126: #1 through to #7 TIPS: p118 #17, #18