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seiche
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I know that if you have x-2, that's the same thing as saying 1/x2. But I'm just wondering what is the mathematical reasoning for why that's true?
Thanks!
Thanks!
seiche said:I know that if you have x-2, that's the same thing as saying 1/x2. But I'm just wondering what is the mathematical reasoning for why that's true?
Thanks!
seiche said:Hmmm... A little dissappointing.
But thanks
[/quote]JSuarez said:1 is not considered a prime because allowing units would ruin the unique factorization theorem.
JSuarez said:There is reason for [tex]0^0 = 1[/tex] that it's more than just a definition. This is a particular (and extreme) case of a combinatorial equality.
JSuarez said:In the context of Analysis, [tex]0^0[/tex] is considered undefined because it stand for a shorthand for a limit of the form:
[tex]
lim_{x\rightarrow a}f(x)^{g(x)}
[/tex]
... It doesn't have directly to do with the continuity [tex]x^y[/tex].
The logic behind negative exponents is based on the fundamental rules of exponents. In general, a negative exponent indicates the reciprocal of the corresponding positive exponent. For example, 2-3 is equivalent to 1/(23), or 1/8. This means that a negative exponent essentially flips the base and exponent to create its reciprocal.
Negative exponents can greatly impact the value of a number. As the exponent decreases, the value of the number decreases exponentially. For example, 2-3 is a much smaller number than 2-1 or 20, even though they all have the same base of 2. This is because the negative exponent is indicating the reciprocal of the positive exponent, resulting in a smaller value.
Yes, negative exponents can be represented in scientific notation. In fact, scientific notation is often used to represent very small numbers, which are often the result of negative exponents. For example, 2-5 can be written as 2 x 10-5 in scientific notation.
Negative exponents are commonly used in scientific and mathematical calculations, as well as in fields such as physics and engineering. They are often used to represent very small values, such as in measurements of subatomic particles or in financial calculations involving interest rates.
Yes, it is possible to have a negative base with a negative exponent. In this case, the exponent acts as a double negative, resulting in a positive value. For example, (-2)-3 is equivalent to -1/(23), which simplifies to -1/8. However, this is only applicable when the base is negative and the exponent is also negative. A negative exponent with a positive base still results in a reciprocal value.