Negative Exponents

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    Related websites

    Why can't polynomials have negative exponents or division by a …

    WEB34. Polynomials are defined as they are for a few distinct reasons: (1) because polynomials as functions have certain properties that your 'polynomials with division' don't have, and (2) because there are other terms for more generalized algebraic forms. First, the properties of polynomials: unlike e.g., 2x − 3 + 3x, polynomials have no poles

    Math.stackexchange.com


    The degree of a polynomial which also has negative exponents.

    WEBHowever when there are negative and positive exponents are present in the function, I want to know the basis that we define the degree. Is the order of a polynomial degree expression defined by the highest magnitude of available exponents?

    Math.stackexchange.com


    Division with negative exponents - Mathematics Stack Exchange

    WEBA term like y−4 y − 4 is essentially saying 1 y4 1 y 4 in the denominator because a negative exponent is the opposite of a positive exponent and you use division. And so here you are dividing by y y four times. So if that's the case, you cross multiply: 1 y4 y4 1 1 y 4 y 4 1 on bottom and then of course to keep balance, you multiply y4 1 y

    Math.stackexchange.com


    Negative Exponents in Binomial Theorem - Mathematics Stack …

    WEBNov 26, 2011 · The binomial expansion "really" sums from 0 0 to ∞ ∞, not 0 0 to n n. In cases where n n is a nonnegative integer, then for k> n k> n, we have that (n k) = 0 (n k) = 0. So terms past k = n k = n do not contribute, and you often see the upper limit "simplified" from ∞ ∞ down to n n. – 2'5 9'2. Commented Nov 26, 2011 at 9:26.

    Math.stackexchange.com


    How to do a modular arithmetic with negative exponents?

    WEB1. IF (and it is a big if) gcd(a, n) = 1 gcd ( a, n) = 1 then we know that there a power k k ( ϕ(n) ϕ ( n) is one such possible k k) so that ak ≡ 1 mod n a k ≡ 1 mod n and that and the aj a j form a group under multiplication modulo n n. And further that aj+k ≡aj mod 25 a j + k ≡ a j mod 25. [It does NOT follow that k = ϕ(n) k = ϕ

    Math.stackexchange.com


    Unresolved,why does negative exponent turns into a fraction?

    WEBOf course, this has its limits. For example, you can't use the basic properties to make sense of $(-8)^{\pi}$ in a reasonable and unambiguous way. Like I mentioned above, after we use the properties to come up with a potential definition, we need to make sure it works, and it just doesn't for some types of exponents.

    Math.stackexchange.com


    How to deal with negative exponents in modular arithmetic?

    WEBRemember that one of the rules of exponents is that $$(x^a)^b = x^{ab}.$$ So we can rewrite $$208 \cdot 2^{-21} \pmod{421}$$ as $$208 \cdot (2^{-1})^{21} \pmod{421}.$$ You can then solve for the modular multiplcative inverse by one of a few techniques, including, as you note, the Extended Euclidean Algorithm.

    Math.stackexchange.com


    How would you explain to a 9th grader the negative exponent rule?

    WEBJan 8, 2014 · In mathematics, the more ways you can explain something, the more likely something will stick. I would start with powers of 10, as suggested by Gina. Review the meaning of positive integer exponents as repeated multiplications of the base. Working backwards, negative exponents are repeated divisions by the base. So $10^3 = 1000$, …

    Math.stackexchange.com


    How do you compute negative numbers to fractional powers?

    WEBIn the first convention, 'continuity' is important. If two exponents are 'near' each other, then they should produce 'nearby' values when used to exponentiate. However, despite the fact $2/3$, $3/5$, and $\pi/5$ are all similarish in size, $(-5)^{2/3}$ and $(-5)^{3/5}$ are widely separated by the fact one 'should' be positive and the other

    Math.stackexchange.com


    Why do negative exponents work the way they do? [closed]

    WEBWe'd like this law to continue to hold when we define xα for negative α, unless there's a good reason it shouldn't. If we do want it to continue to hold for negative exponents, then whatever we decide that x − 1 should mean, it should obey the same law: x − 1 ⋅ x2 = x − 1 + 2 = x1 = x. and so x − 1 = 1 x is the only choice.

    Math.stackexchange.com


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