Starter 1. 3. 2. 4. Chapter 7: Laws of Algebra Essential Question How can you simplify expressions involving exponents?
Title Page Number Investigation Discovering Index Laws I can: Multiply numbers with the same base. Divide numbers with the same base. Raise a power to another power.
Investigation Discovering Index Laws (p130 131) We can discover some laws for indices by considering several examples and looking for patterns. 1. Copy and complete: (a) 22 x 23 = (2 x 2) x (2 x 2 x 2) = 25 (b) 33 x 31 = ________________ = _____ (c) a3 x a4 = ________________ = _____ In general, am x an = _______ 2. Copy and complete:
(a) 25 = 2 x 2 x 2 x 2 x 2 = 22 23 = 2x2x2 (b) 54 = = 51 (c) a5 = = a2 (d) x7 = =
x4 In general, am = an 3. Copy and complete: (a) (73)2 = 73 x 73 = (7 x 7 x 7) x (7 x 7 x 7) = _____ (b) (32)4 = _____ = _________________ = _____ (c) (a4)3 = _____ = _________________ = ______ In general, (am)n = ________ Simplify using the laws of indices:
Example 1: (a) 23 x 22 Example 2: (a) 35 33 Example 3:
(b) x4 x x5 (b) p7 p3 (a) (23)2 (b) (x4)5 Example 4: Express as a power of a (a6 x a2)3 1.
Independent Practice Construct a foldable for the first 3 rules with two examples inside 2.
p132 - 133 #1 - 9 Starter Top 3 HW HW Quiz Homework Quiz Simplify using the index laws. Please complete 5 of the 6 questions.
1. c6 c4 2. (k4)2 k 3. (z6)5 4. 24w2z4 6w2z3 5. Express as a power of 2. 23 x 2 7 2 x 22 6. Express as a power of x.
x10 x (x2)5 x Homework Quiz Simplify using the index laws. Please complete 5 of the 6 questions. 1. b8 b5 2. (p2)2 x p2 3. n2 x n3 x n5
4. h14 x h2 (h4)2 5. Express as a power of 2. (211)2 x 23 (26)3 x 24 6. Express as a power of x. (x6 x x7)2 7B Expansion Laws I can:
Apply expansion laws to remove brackets and simplify an expression. Apply the zero index law to simplify expressions. 7B Expansion Laws Express in simplest form, without brackets. Example 1 Example 3
(ab)5 (2xy)3 Example 2 Example 4 m n
( ) 4 2 b ( ) 3
7B Expansion Laws Express in simplest form, without brackets. Example 5 (3a2)2 Example 6 (4a2b)3 7C Zero Index Law Investigation 1. Find the value of:
(a) 2 (b) 3 (c) 4 (d) - 8 (e) - 5(f) (g) 7 2 3 4 -8 -5
7 57 57 2. Copy and complete: When a non-zero value is divided by itself, the result is always _______. a3 3. Use question 2 to complete: =
a3 3 a 4. Use an index law to show that: = a0 3 a 5. Use questions 3 and 4 to write the rule for: a0 = In fact, any non-zero number raised to the power of 0 is equal to 1. For example:
100 = 1 3.4520 = 1 723 538 5920 = 1 1. Independent Practice Add the
zero index law to your foldable (2 examples inside) 2. p134-135 #1-5 3. p136 #1-3 Starter Top 3 HW
HW Quiz 7D Negative Index Law Investigation I can: Apply negative index law to simplify. Apply the distributive property to expand and simplify expressions. 7D Negative Index Law Investigation 1. Consider the fraction
(a) By expanding and then cancelling common factors, show (b) Use an index law to show that (c) Copy and complete: 2. Write the law for negative indices: 7D Negative Index Law Investigation Example 1: Example 4:
6-2 7 8 Example 2: 8ab-1 Example 3: 8(ab)-1
2 () 7E Distributive Property Order of Operations 6(3 + 5) = 6(8) = 48
Distributive Property 6(3 + 5) = 6(3) + 6(5) = 18 + 30 = 48 Why distribute when order of operations is faster ? Use the distributive property to simplify. Example 5: 3(x + 7)
Example 7: 7(2m + 3y - 4) Example 6: 2(a + 4) 1. Independent Practice Add the negative
index law to your foldable (2 examples inside) 2. p138-139 #1-3 3. P140-141 #3-6 4. Ch.7 Test (Nov. 27 sec. 1-4, Nov. 28 sec. 5)