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       Exponents                                                               
                          
Rules for Positive Exponents
                        Exponents (Positive)- Simplify, or Combine Like Terms
                        Exponents (Positive)- Add & Subtract Polynomials, also Combine Like Terms
                        Exponents (Positive)- Multiply Polynomials, and Monomials
                        Exponents (Positive)- Divide Polynomials by Monomials
                        Rules for Negative Exponents & Zero Exponents
                        Exponents (Negative & Zero)- Simplify
                        Scientific Notation



Rules for Positive Exponents____Exponents (Positive)- Simplify, or Combine Like Terms
My intention is for the next two videos to be covered in succession;
the second video assumes familiarity with concepts introduced in the first.
I cover the rules for operations with positive exponents, from adding (or subtracting), to multiplying, raising to a power, and finally dividing. I develop the rules based on longer methods, which are easier to understand, and then the "shortcut" rules, which are faster and easier to write. As usual, it may be helpful to print the Sheets Used in Video prior to viewing so you can write notes while working along with the video.

While there is no practice worksheet for this video, the practice is intended for after viewing the second video, which goes over applying these rules in a variety of situations.
 
 
Sheets Used in Video
Sheets Used in Video (Answer Key)
 








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Applying the exponent rules covered in the previous video, Exponents (Positive)- Rules, I go through 13 examples. Some problems involve more than one rule to simplify the expression. The practice worksheet has three columns of six problems each, and each column has a similar variety of problems. Thus, I suggest checking as you go, pausing or taking a break between columns, and then trying to proceed without looking at notes or examples. This helps to promote your long-term memory on the topic.
 
Sheets Used in Video
Sheets Used in Video (Answer Key)


Exponents (Positive)- Simplify, or Combine Like Terms
Exponents (Positive)- Simplify, or Combine Like Terms (Answer Key)


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Exponents (Positive)- Add & Subtract Polynomials, also Combine Like Terms
I cover 3 problems to illustrate the similarity between combining like terms and adding or subtracting polynomials. Then I go over 11 more problems of increasing complexity, with the last two involving the meaning of "subtract from," which can be confusing.

The practice worksheets are offered in two versions, with the second perhaps a bit more challenging. Each sheet has two columns of five problems each, and a similar variety of problems in each column. As usual, I recommend checking as you go, and taking a break between each column. Try to resume work without looking at notes or examples; promote that long-term memory.

 
Sheets Used in Video
Sheets Used in Video (Answer Key)



Exp. (Pos.)- Add & Sub. Polynomials, also Comb. Like Terms (A- Less Difficult)
Exp. (Pos.)- Add & Sub. Poly., also Comb. Like Terms (A- Less Dif.) (Ans. Key)


Exp. (Pos.)- Add & Sub. Polynomials, also Comb. Like Terms (B- More Difficult)
Exp. (Pos.)- Add & Sub. Poly., also Comb. Like Terms (B- More Dif.)(Ans. Key)


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Exponents (Positive)- Multiply Polynomials, and Monomials
I go over 10 examples to illustrate some things to keep in mind as you multiply and simplify. After that I cover an additional 7 problems in a "Mixed Practice." The last 7 are basically a review of the previous concepts. The practice worksheet has three columns of seven problems each, and each column has a similar variety of problems. Thus, I suggest checking as you go, pausing or taking a break between columns, and then trying to proceed without looking at notes or examples. This helps to promote your long-term memory on the topic.
 
Sheets Used in Video
Sheets Used in Video (Answer Key)



Exponents (Positive)- Multiply Polynomials, and Monomials
Exponents (Positive)- Multiply Poly., and Monomials (Answer Key)

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Exponents (Positive)- Divide Polynomials by Monomials
I go over 7 examples to illustrate some things to keep in mind as you divide and simplify. After that I cover an additional 3 problems in a "Mixed Practice." The last 3 are basically a review of the previous concepts, but the answers may look slightly different. The practice worksheet has three columns of five problems each, and each column has a similar variety of problems, although answers may look slightly different. I suggest checking as you go, pausing or taking a break between columns, and then trying to proceed without looking at notes or examples; promote your long-term memory on this topic.
 
Sheets Used in Video
Sheets Used in Video (Answer Key)



Exponents (Positive)- Divide Polynomials by Monomials
Exponents (Positive)- Divide Polynomials by Monomials (Answer Key)



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Rules for Negative Exponents & Zero Exponents____Exponents (Negative & Zero)- Simplify
  I include both topics in one video, as the development of the rules only takes five minutes.
Based on rules for positive exponents (with which you should be familiar), I develop the rule for negative exponents, and the rule for zero exponents; this takes the first 5 minutes. In the rest of the video, I go over about 20 examples of simplifying what you are given when negative and/or zero exponents are involved. Because such a wide variety of problems are possible with negative and zero exponents, I've made two sheets for practice. The second may be slightly more challenging than the first. Upon completing the first sheet, you have done a good variety of problems. I advise a break of some duration prior to attempting the second sheet; promote your long-term memory.
 
Sheets Used in Video
Sheets Used in Video (Anwer Key)



Exponents (Negative & Zero)- Simplify A
Exponents (Negative & Zero)- Simplify A (Answer Key)


Exponents (Negative & Zero)- Simplify B
Exponents (Negative & Zero)- Simplify B (Answer Key)


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Scientific Notation
I give two brief examples of numbers (from the sciences) written in both standard and scientific notations. Then I go over three examples of converting from standard to scientific notation, and three examples of converting from scientific to standard notation. The practice worksheet has two columns, each with six problems. Each column has three of each type of conversion. I recommend a break of some duration between completing the columns; this helps to develop your long-term memory.
 
Sheets Used in Video
Sheets Used in Video (Answer Key)


Scientific Notation
Scientific Notation (Answer Key)


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