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Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :

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Presentation on theme: "Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :"— Presentation transcript:

1 Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :

2 Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 : - When you multiply like variables you ADD their exponents

3 Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 : - When you multiply like variables you ADD their exponents - When you divide like variables you SUBTRACT their exponents

4 Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 : - When you multiply like variables you ADD their exponents - When an exponent is raised to another exponent, you MULTIPLY exponents - When you divide like variables you SUBTRACT their exponents

5 Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 : - When you multiply like variables you ADD their exponents - When an exponent is raised to another exponent, you MULTIPLY exponents - When you divide like variables you SUBTRACT their exponents - When a variable has a negative exponent, you change its position in a fraction and the exponent becomes positive.

6 Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 : - When an exponent is raised to another exponent, you MULTIPLY exponents - When you divide like variables you SUBTRACT their exponents - When a variable has a negative exponent, you change its position in a fraction and the exponent becomes positive.

7 Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 : - When an exponent is raised to another exponent, you MULTIPLY exponents - When a variable has a negative exponent, you change its position in a fraction and the exponent becomes positive.

8 Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 : - When a variable has a negative exponent, you change its position in a fraction and the exponent becomes positive.

9 Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 :

10 Algebraic Expressions – Rules for Exponents Let’s review the rules for exponents you learned in Algebra 1 : What we are going to do in Pre – Calc is take these rules and combine them into multi – step problems that might have all four rules utilized.

11 Algebraic Expressions – Rules for Exponents Example # 1 :

12 Algebraic Expressions – Rules for Exponents Example # 1 : Since everything is multiplied, we can multiply all integers, and all like variables.

13 Algebraic Expressions – Rules for Exponents Example # 1 :

14 Algebraic Expressions – Rules for Exponents Example # 1 : Example # 2 :

15 Algebraic Expressions – Rules for Exponents Example # 1 : Example # 2 : Don’t PANIC !!! The rule for multiplying like variables still applies. Exponents can be algebraic, integers, or fractions

16 Algebraic Expressions – Rules for Exponents Example # 1 : Example # 2 : Don’t PANIC !!! The rule for multiplying like variables still applies. Exponents can be algebraic, integers, or fractions We will still ADD exponents

17 Algebraic Expressions – Rules for Exponents Example # 1 : Example # 2 : Now just treat the exponent like an algebraic expression where we combine like terms… We will still ADD exponents

18 Algebraic Expressions – Rules for Exponents Example # 3 : When you have imbedded parentheses and exponents outside, start with the innermost set and work your way “out”.

19 Algebraic Expressions – Rules for Exponents Example # 3 : Evaluate this first, applying the exponent outside to ALL of the terms inside.

20 Algebraic Expressions – Rules for Exponents Example # 3 :

21 Algebraic Expressions – Rules for Exponents Example # 3 : I like to multiply what is inside the brackets before I apply the outside exponent.

22 Algebraic Expressions – Rules for Exponents Example # 3 : Apply the outside exponent.

23 Algebraic Expressions – Rules for Exponents Example # 3 :

24 Algebraic Expressions – Rules for Exponents Example # 4 : There are two ways to attack this problem. 1.Apply the division rule using negative exponents. 2.Use the negative exponent rule first, then apply the division rule.

25 Algebraic Expressions – Rules for Exponents Example # 4 : There are two ways to attack this problem. 1.Apply the division rule using negative exponents. 2.Use the negative exponent rule first, then apply the division rule.

26 Algebraic Expressions – Rules for Exponents Example # 4 : There are two ways to attack this problem. 1.Apply the division rule using negative exponents. 2.Use the negative exponent rule first, then apply the division rule. I applied the negative exponent rule and moved any variable with a negative exponent to the other part of the fraction and made the exponent positive…

27 Algebraic Expressions – Rules for Exponents Example # 4 : There are two ways to attack this problem. 1.Apply the division rule using negative exponents. 2.Use the negative exponent rule first, then apply the division rule. Apply the normal division of like variables rule…

28 Algebraic Expressions – Rules for Exponents Example # 5 : This problem has a few rules to apply, apply the exponent to each parentheses first…

29 Algebraic Expressions – Rules for Exponents Example # 5 : This problem has a few rules to apply, apply the exponent to each parentheses first… When you have an integer to the ½ power, it is the square root of the integer.

30 Algebraic Expressions – Rules for Exponents Example # 5 : This problem has a few rules to apply, apply the exponent to each parentheses first… Now you divide your variables…

31 Algebraic Expressions – Rules for Exponents Example # 5 : This problem has a few rules to apply, apply the exponent to each parentheses first… Anything to the zero power = 1, and it is not necessary to change improper fractions to mixed numbers…

32 Algebraic Expressions – Rules for Exponents Example # 6 :

33 Algebraic Expressions – Rules for Exponents Example # 6 : On this one I would reduce any integer fraction first…

34 Algebraic Expressions – Rules for Exponents Example # 6 : On this one I would reduce any integer fraction first…

35 Algebraic Expressions – Rules for Exponents Example # 6 : Now apply the negative exponent outside…

36 Algebraic Expressions – Rules for Exponents Example # 6 : Move your negative exponent variables…

37 Algebraic Expressions – Rules for Exponents Example # 6 : Apply multiplication and division of variables rules…


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