Rules of Exponents Part 1[Algebra 1](In Class Version).notebook. August 22, 2017 WARM UP. Simplify using order of operations. SOLUTION.
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1 WARM UP Simplify using order of operations. Aug 22 3:22 PM 1
2 Aug 22 4:09 PM 2
3 WARM UP a) The equation 3(4x) = (4x)3 illustrates which property? b) Which property of real numbers is illustrated by the equation : Aug 22 4:10 PM 3
4 c) If M, P and Q represent integers, M = P and P = Q then M = Q is an example of which property? d) The equation 5 + (3x + 4) = (5 + 3x) + 4 illustrates which property? Aug 22 4:27 PM 4
5 Homework Assignment The following examples have to be copied for next class Example 3 Example 5 Example 6 Example 7 Example 8 Example 10 Example 11 Example 14 Example 15 Example 17 The examples must be copied and ready for me to check once you come to class. Aug 19 3:11 PM 5
6 Rules of Exponents Aug 19 6:29 AM 6
7 The Zero Exponent Rule If b is any real number other than 0, then also zero raised to the zeroth power is undefined. is undefined Aug 19 7:22 AM 7
8 EXAMPLE 1 Simplify : Aug 19 7:25 AM 8
9 EXAMPLE 2 Simplify : 1 Aug 15 12:15 PM 9
10 EXAMPLE 3 Simplify : 1 Jul 17 6:25 PM 10
11 EXAMPLE 4 Simplify : 1 Jul 17 6:21 PM 11
12 EXAMPLE 5 Simplify : 1 Jul 17 6:24 PM 12
13 Opposite of a Power Aug 22 1:47 PM 13
14 EXAMPLE 6 Simplify : Raise 2 to the 3 rd power then take the opposite of this number. Aug 22 1:48 PM 14
15 EXAMPLE 7 Simplify : Raise 6 to the 0 th power then take the opposite of this number. Aug 22 1:48 PM 15
16 Changing the sign of an Exponent If a term in the numerator is moved to the denominator the exponent will now have the opposite sign. (If the exponent was negative it will become positive and vice versa.) The same is true if a term in the denominator is moved to the numerator the exponent will now have the opposite sign. Jul 18 10:28 AM 16
17 EXAMPLE 8 For the following expression if a term was originally in the numerator move the term to the denominator. If a term was originally in the denominator move the term to the numerator. Rewrite the expression so that every term has an exponent. Jul 18 10:33 AM 17
18 Move only the terms in the numerator to the denominator. Keep in mind the only thing that should change is the exponent will now have the opposite sign. Now move the terms that were originally in the denominator to the numerator. Keep in mind the only thing that should change is the exponent will now have the opposite sign. Jul 18 10:43 AM 18
19 EXAMPLE 9 Rewrite the expression with only positive exponents : Rewrite the expression so that every term has an exponent. Move any term to the denominator that has a negative exponent in the numerator. Notice that the 5 did not move to the denominator, we only move a term if the exponent is negative, not the number itself. Aug 15 2:01 PM 19
20 Move any term to the numerator that has a negative exponent in the denominator. Aug 15 2:02 PM 20
21 EXAMPLE 10 Rewrite the expression with only positive exponents : Rewrite the expression so that every term has an exponent. Move any term to the denominator that has a negative exponent in the numerator. Aug 15 2:08 PM 21
22 EXAMPLE 11 Rewrite the expression with only positive exponents : Move any term to the denominator that has a negative exponent in the numerator. Whenever the numerator does not have a value place a 1 in the numerator. Jul 17 7:23 PM 22
23 EXAMPLE 12 Rewrite the expression with only positive exponents : Move any term to the denominator that has a negative exponent in the numerator. Whenever the numerator does not have a value place a 1 in the numerator. Notice that only the exponent has an opposite sign, the 2 has the same sign. Jul 18 11:01 AM 23
24 Product Rule with the same base When multiplying exponential expressions with the same nonzero base, ADD the exponents. Use this sum as the exponent of the common base. Aug 19 6:58 AM 24
25 EXAMPLE 13 Simplify : Since we are multiplying powers with the same bases use the product to simplify the expression. Aug 19 7:10 AM 25
26 EXAMPLE 14 Simplify : Rewrite the expression so that every term has an exponent. Rearrange so that like terms are grouped together. Because we are multiplying powers with the same base apply the product rule. Aug 19 7:15 AM 26
27 EXAMPLE 15 Simplify : Rewrite the expression so that every term has an exponent. Rearrange so that like terms are grouped together. Because we are multiplying powers with the same base apply the product rule. Jul 17 5:37 PM 27
28 Quotient Rule with the same base When dividing exponential expressions with the same nonzero base, SUBTRACT the exponent in the numerator minus the exponent in the denominator. Use the difference as the exponent of the common base. Aug 19 7:17 AM 28
29 EXAMPLE 16 Simplify : Since the bases are the same we can keep the common base and subtract the exponents. Aug 19 7:18 AM 29
30 EXAMPLE 17 Simplify the expression the final answer should only have positive exponents. Rewrite the expression so that every term has an exponent. Rearrange so that like terms are grouped together. Apply the quotient rule the fraction bar implies dividing. Jul 18 11:57 AM 30
31 Rewrite the expression so that all the exponents are positive. Keep in mind that only negative exponents are going to be moved negative numbers remain in place. Jul 18 11:34 AM 31
Simplifying Square Root Expressions[In Class Version][Algebra 1 Honors].notebook August 26, Homework Assignment. Example 5 Example 6.
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