MATHCP Algebra I  - Unit 13: Law of Exponents
1)

Explain why laws of exponents are needed.


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2)

Give an example of how laws of exponents can be used in the real world. 


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Multiplying Monomials


3)

What does an exponent tell you to do? 


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4)

Name the base and the exponent for the expression 43, and then evaluate. 


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5)

Explain the "product of powers" rule. 


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In the following problems, use the "product of powers" rule to simplify each expression.


6)

Simplify.


7)

Simplify.


8)

Simplify.


9)

Simplify.


Extra Practice:  Check with you instructor to see if s/he would like for you to do some extra practice problems.  Click here to view the practice worksheet.


Geometry Connection

Find the area of each rectangle and the volume of the rectangular solid in the following questions.


10)

What is the area of the rectangle (A = lw)?


11)

What is the volume of the rectangular solid (V = lwh)?


12)

What is the area of the rectangle (A = lw)?


Powers and Products


13)

Explain the "power-of-a-power" rule. 


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14)

Explain the "power-of-a-product" rule. 


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15)

Simplify.


16)

Simplify.


17)

Simplify.


18)

Simplify.


19)

Simplify.


Extra Practice:  Check with you instructor to see if s/he would like for you to do some extra practice problems.  Click here to view the practice worksheet.

Powers of (–1)


20)

Explain the pattern of even and odd exponents on negative bases. 


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21)

Simplify.


22)

Simplify.


23)

Simplify.


24) Simplify: using more than one rule.

Note:  The carat(^) is accessed on the keyboard using Shift + 6.

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25)

Simplify: using more than one rule.

Note:  The carat(^) is accessed on the keyboard using Shift + 6.


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Review


26)

Evaluate. 

Click here to review the unit content explanation for Expressions, Variables, and Properties.


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27)

Evaluate.  5 – (–3.6)

Click here to review the unit content explanation for Expressions, Variables, and Properties.


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28)

Let x = 8, y = –2, and z = –5, and then evaluate xy + 3z.

Click here to review the unit content explanation for Expressions, Variables, and Properties.


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29)

Simplify.  (–4x – 3y) – (–7x – 2y)

Click here to review the unit content explanation for Expressions, Equations, and Inequalities.


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30)

Simplify.  (–2m + 4n) + (3m – 5n) – (7m + 6n)

Click here to review the unit content explanation for Expressions, Equations, and Inequalities.


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31)

Write an equation for the following situation, and then solve the equation. Pam has $32. How many hours can Pam bowl if bowling costs $5 plus $3 per hour? 

Click here to review the unit content explanation for Integers and Equations.


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In the following problems, solve each equation.   

Click here to review the unit content explanation for Rational Numbers and Exponents.


32)

Solve for “m”.


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33)

Solve for “b”.  –4b = 16 


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34)

Solve for “p”.


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35)

Solve for “n”.


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36)

Solve for “r”.  6 – 2r = 42


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37)

Solve for “b”.  4b + 1 = 12 + 5


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38)

Solve for “x”.   5(x + 1) + 2 = 2x + 11 


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39)

Solve the system of equations using elimination.

Click here to review the unit content explanation for More Systems of Equations.


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40)

Explain how you used the elimination process to solve the previous problem.

Click here to review the unit content explanation for More Systems of Equations.


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