# Starter - Weebly

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)

## Recently Viewed Presentations

• "The part of the diffusion curve from about 10 percent to 20 percent adoption is the heart of the diffusion process. After that point, it is often impossible to stop the further diffusion of a new idea, even if one...
• Climograph Activity! Directions: Study the climographs on page 30. You will make three climographs of three cities. The cities are Church Hill, TN, Myrtle Beach, SC, and Denver, CO. The statistics to make your climographs are on the next page....
• STANFORD-BINET Intelligence Scale evolusi 1904 1905 1908 1911 1916 Binet mendapat tugas dari pemerintah Perancis Terbit skala Binet yang terdiri 30 item Terbit hasil revisi bersama Theodore Simon Ada pembatasan usia subjek Ada pengelompokan item Perluasan proses mental yang diukur...
• Also by comparing 1000-500 mb thickness and surface pressure isobars, which have historically been plotted together on weather charts (MSLP/1000-500 thickness chart) 500-1000mb Thickness In addition to isotherms on a constant pressure surface, we can look at thickness compared to...
• 'Center of Projection' 'Pinhole' Model: Rays copy scene onto 'film' Ray Scene Sensor Lens 'Center of Projection' Angle( , ) Ray Position (x,y) 'Pinhole' Model: Rays copy scene onto 'film' Scene Sensor Lens 'Center of Projection' Angle( , ) Ray...
• A hockey puck on the table, experiencing almost nofriction, appears to not be moving but we know the train is moving so the puck must also be moving at 20 m/s relative to the ground. Both velocities for the air...
• When parking uphill with a curb on your right, which way should the wheels be turned? Question 7. Turned to the left, away from the curb. If your BAC is .05% the risk of you causing a motor vehicle collision....
• Overview In order to take the following leave you must go through your regional substitute coordinator and/or the HR director, approvals by your building principal is not authorization.