= = 3 3 x 3x 3 x 3x 3 x 3x 3 x 3x 3 x 3x 3 x 3x 3

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

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

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

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

#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.

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)

Page 120 #11 QuotientExpanded FormSingle Power 55  5355     2 6 p 8  p 5 Own example (-2) 5 x (-2) 2

#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.

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)

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

#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

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

The bases must be the same!

Can you simplify this?

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