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Negative Exponents (page 2 of 5) Sections: Basics, Negative exponents, Scientific notation, Engineering notation, Fractional exponents A negative exponent just means that the base is on the wrong side of the fraction line, so you need to flip the base to the other side. For instance, "x^{–2}" (ecks to the minus two) just means "x^{2}, but underneath, as in 1/(x^{2})".
Note that the "2" above does not move with the variable; the exponent is only on the "x".
Unlike the previous exercise, the parentheses meant that the negative power did indeed apply to the three as well as the variable.
This one can also be done as: Copyright © Elizabeth Stapel 20002016 All Rights Reserved Since exponents indicate multiplication, and since order doesn't matter in multiplication, there will often be more than one sequence of steps that will lead to a valid simplification of a given exercise. Don't worry if the steps in your homework look quite different from the steps in a classmate's homework. As long as your steps were correct, you should both end up with the same answer. You can use the Mathway widget below to practice simplifying expressions with negative exponents. Try the entered exercise, or type in your own exercise. Then click the "paperairplane" button to compare your answer to Mathway's. (Or skip the widget and continue with the lesson.)
(Click here to be taken directly to the Mathway site, if you'd like to check out their software or get further info.) By the way, now that you know about negative exponents, you can understand the logic behind the "anything to the power zero" rule: Anything to the power zero is just "1". Why is this so? There are various explanations. One might be stated as "because that's how the rules work out." Another would be to trace through a progression like the following: 3^{5}
= 3^{6}
÷ 3 = 3^{6}
÷ 3^{1}
= 3^{6–1}
= 3^{5}=
243 Then logically 3^{0} = 3^{1} ÷ 3^{1} = 3^{1–1} = 3^{0} = 1. A negativeexponents explanation of the "anything to the zero power is just 1" might be as follows: m^{0} = m^{(n – n)} = m^{n} × m^{–}^{n} = m^{n} ÷ m^{n} = 1 ...since anything divided by itself is just "1". Another comment: Please don't ask me to "define" 0^{0}. There are at least two ways of looking at this quantity:
As far as I know, the "math gods" have not yet settled on a "definition" of 0^{0}. In fact, in calculus, "0^{0}" will be called an "indeterminate form". If this quantity comes up on class, don't assume: ask your instructor what you should do with it. << Previous Top  1  2  3  4  5  Return to Index Next >>



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