Overview
On this page, we review important properties of exponents.
Basic Learning Objectives
These are the tasks you should be able to perform with reasonable fluency when you arrive at your next class meeting. Important new vocabulary words are indicated in italics.
- Correctly evaluate powers involving negative signs.
- Combine products and quotients of powers with the same base.
- Simplify a power of a power.
- Expand a power of a product or quotient.
Advanced Learning Objectives
In addition to mastering the basic objectives, here are the tasks you should be able to perform after class, with practice:
- Simplify complex fractions involving several powers of several variables, using the order of operations.
- Be aware that the exponent in a power of a sum or difference can never be directly distributed. For example, \((x+y)^2=x^2+2xy+y^2\), which is not the same as \(x^2+y^2\)! Similarly, \(\sqrt{x+y}=(x+y)^{1/2}\) cannot be split and has to be left like this.
To prepare for class
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Watch the following video (by patrickJMT) pointing out some common mistakes involving exponents, especially when negative signs are involved:
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Watch the following videos (by Tyler Wallace) which explain how to simplify products and quotients involving powers with the same base:
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Watch the following video (by Tyler Wallace) which explains how to “bring in” exponents to products, quotients, and other powers:
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Watch the following video (by Tyler Wallace) which explains why an exponent of 0 gives a result of 1:
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Watch the following video (by Tyler Wallace) which explains how to deal with negative exponents:
After class
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Watch the following video (by Tyler Wallace) which summarizes all important exponent properties and goes through some more complicated examples (please ignore the last example after 3:03 in the video, as it contains a small error):
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Watch the following videos (by patrickJMT) which show some more complicated example calculations:
