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Course: Grade 7 (VA SOL) > Unit 8
Lesson 3: Negative exponentsNegative exponents review
Review the basics of negative exponents and try some practice problems.
Definition for negative exponents
We define a negative power as the multiplicative inverse of the base raised to the positive opposite of the power:
Want to learn more about this definition? Check out this video.
Examples
Some intuition
So why do we define negative exponents this way? Here are a couple of justifications:
Justification #1: Patterns
Notice how is divided by each time we reduce . This pattern continues even when is zero or negative.
Justification #2: Exponent properties
Recall that . So...
We also know that
And so we get .
Also, recall that . So...
And indeed, according to the definition...
Want to join the conversation?
- how can you say that 1/1/9 is 9??(18 votes)
- 1/(1/9). How many 9ths are in one whole? Nine.(78 votes)
- how do we divide exponents by exponents?(9 votes)
- you subtract the exponent on the top from the exponent on the bottom.(31 votes)
- What happens when zero is put to the zero power, for example 0^0(5 votes)
- Interesting question! Consider the following two rules:
1) Any nonzero number to the zero power is 1.
2) Zero to any positive power is 0.
If we try to extend both rules to define 0^0, we get different answers. So should 0^0 be 0, 1, or something else? Because of this situation, it is best to call 0^0 indeterminate (though 0^0 is often interpreted as 1).
Have a blessed, wonderful day!(30 votes)
- wowzers i really had a blast(14 votes)
- how much math is too much math?(10 votes)
- any math. all math is to much math(8 votes)
- Me too but I guess we just have to learn it(4 votes)
- if a exponent is negative what happens to the base(4 votes)
- The base remains the same. As the page explains, a negative exponent just means "the multiplicative inverse of the base raised to the positive opposite of the power". So a^(-b) = 1/(a^b). The base, a, doesn't change. Only its place in the expression changes.(10 votes)
- Man, I thought I was going lose!(8 votes)
- i need more practice(7 votes)
- this was easy if you pay attention to the promblem.(7 votes)