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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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**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

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**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

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**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 - When an exponent is raised to another exponent, you MULTIPLY exponents

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**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 - 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.

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**Algebraic Expressions – Rules for Exponents**

Let’s review the rules for exponents you learned in Algebra 1 : - When you divide like variables you SUBTRACT their exponents - 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.

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**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.

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**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.

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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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**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.

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**Algebraic Expressions – Rules for Exponents**

Example # 1 :

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**Algebraic Expressions – Rules for Exponents**

Example # 1 : Since everything is multiplied, we can multiply all integers, and all like variables.

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**Algebraic Expressions – Rules for Exponents**

Example # 1 :

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**Algebraic Expressions – Rules for Exponents**

Example # 1 : Example # 2 :

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**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

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**Algebraic Expressions – Rules for Exponents**

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

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**Algebraic Expressions – Rules for Exponents**

Example # 1 : Example # 2 : We will still ADD exponents Now just treat the exponent like an algebraic expression where we combine like terms…

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**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”.

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**Algebraic Expressions – Rules for Exponents**

Example # 3 : Evaluate this first, applying the exponent outside to ALL of the terms inside.

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**Algebraic Expressions – Rules for Exponents**

Example # 3 :

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**Algebraic Expressions – Rules for Exponents**

Example # 3 : I like to multiply what is inside the brackets before I apply the outside exponent.

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**Algebraic Expressions – Rules for Exponents**

Example # 3 : Apply the outside exponent.

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**Algebraic Expressions – Rules for Exponents**

Example # 3 :

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**Algebraic Expressions – Rules for Exponents**

There are two ways to attack this problem. Apply the division rule using negative exponents. Use the negative exponent rule first, then apply the division rule. Example # 4 :

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**Algebraic Expressions – Rules for Exponents**

There are two ways to attack this problem. Apply the division rule using negative exponents. Use the negative exponent rule first, then apply the division rule. Example # 4 :

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**Algebraic Expressions – Rules for Exponents**

There are two ways to attack this problem. Apply the division rule using negative exponents. Use the negative exponent rule first, then apply the division rule. Example # 4 : 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…

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**Algebraic Expressions – Rules for Exponents**

There are two ways to attack this problem. Apply the division rule using negative exponents. Use the negative exponent rule first, then apply the division rule. Example # 4 : Apply the normal division of like variables rule…

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**Algebraic Expressions – Rules for Exponents**

This problem has a few rules to apply, apply the exponent to each parentheses first… Example # 5 :

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**Algebraic Expressions – Rules for Exponents**

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

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**Algebraic Expressions – Rules for Exponents**

This problem has a few rules to apply, apply the exponent to each parentheses first… Example # 5 : Now you divide your variables…

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**Algebraic Expressions – Rules for Exponents**

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

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**Algebraic Expressions – Rules for Exponents**

Example # 6 :

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**Algebraic Expressions – Rules for Exponents**

Example # 6 : On this one I would reduce any integer fraction first…

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**Algebraic Expressions – Rules for Exponents**

Example # 6 : On this one I would reduce any integer fraction first…

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**Algebraic Expressions – Rules for Exponents**

Example # 6 : Now apply the negative exponent outside…

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**Algebraic Expressions – Rules for Exponents**

Example # 6 : Move your negative exponent variables…

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**Algebraic Expressions – Rules for Exponents**

Example # 6 : Apply multiplication and division of variables rules…

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MTH 091 Sections 3.1 and 9.2 Simplifying Algebraic Expressions.

MTH 091 Sections 3.1 and 9.2 Simplifying Algebraic Expressions.

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