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Integer Exponents
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What you will learn from this videoWhat you will learn
- About negative exponents!
- How to do operations with negative exponents.
- That we can use this knowledge to help us look at microorganisms, help wildlife, and even learn about elements!
- Discussion Questions
Before Video
What is an exponent? What are the names of the different parts of an exponent?
ANSWERExponents represent repeated multiplication. Exponents have a base and a power.
4 is the base (the number being multiplied) and 9 is the power (the number of times 4 is multiplied).
49 = 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 × 4 = 262,144
When I multiply two exponents with the same base, I can keep the same base and add the powers. Sample answer: 2^{3} × 2^{2} = 2^{3} + 2 = 2^{5}.
When I divide two exponents with the same base, I can keep the same base and subtract the powers. Sample answer: 2^{5} ÷ 2^{3} = 2^{5 – 3}= 2^{2}.
After Video
What is the relationship between the following expressions: 2^{3}, 2^{2}, 2^{1}, 2^{0}, 2^{–1}, 2^{-2}ANSWEREach exponential expression is 12 the value of the one before it: 8, 4, 2, 1, [ggfrac]1/2[/ggfrac], [ggfrac]1/4[/ggfrac].
A number raised to a negative power is the same as 1 over that same number raised to the positive power.
2 ×[ggfrac]1/10^{23} or [ggfrac]2/10^{23}[/ggfrac]
The rule doesn’t change. Keep the same base and add the powers. The only change is that I may be adding a negative number.
The rule doesn’t change. Keep the same base and subtract the powers. The only change is that I may be subtracting a negative number.
- Vocabulary
- Exponential expression DEFINE
An exponential expression is another way of showing repeated multiplication. 2^{3} = 2 × 2 × 2.
- Base DEFINE
In an exponential expression, the base represents the number that is being multiplied. In 2^{3}, the 2 is the base.
- Power DEFINE
In an exponential expression, the power represents the number of times the base is multiplied by itself. In 2^{3}, the 3 is the power.
- Product of powers rule DEFINE
A rule of arithmetic with exponential expressions. It says that when you multiply two exponential expressions with the same base, you can keep the base and add the exponents.
- Quotient of powers rule DEFINE
A rule of arithmetic with exponential expressions. It says that when you divide two exponential expressions with the same base, you can keep the base and subtract the exponents.
- Equivalent expression DEFINE
Two expressions are equivalent if they represent the same quantity. For example, 2^{3}and 2 × 2 × 2 are equivalent expressions because they are both equal to 8.
- Exponential expression DEFINE
- Reading Material
- Practice Word Problems
- Practice Number Problems
- Lesson Plan
- Teacher Guide
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