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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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Warm up Use the laws of exponents to simplify the following. Answer should be left in exponential form.

Warm up Use the laws of exponents to simplify the following. Answer should be left in exponential form.

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