Nice Math Olympiad Simplification Problem | Fraction Exponents | You Should NOT use Calculators
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Published 2024-04-19
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All Comments (21)
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Это не решение. Видимо он учился на Западе. Сразу кол ему нужно ставить в дневнике.
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Unnecessary lengthy
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Simply you are wasting the time by repenting the trivial steps.
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How is that result simpler than the original? Simplest form technically would be ²(1/9) but without using tetration, surely the simplest form would be 3^(-2/9).
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This is a call nay an appeal to all maths teachers. Please make your presentations shorter , avoid repetition. Your primary responsibilty , if I am not mistaken, is to make maths simpler and attractive . But many times I am forced to move away from many of the posts . A five minute presentation takes half an hour !
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By simplify, I think the kind teacher meant the expression should be written with a rational denominator and in terms of n-th roots of positive integers. So, (1/9)¹ᐟ⁹ = (1/3²)¹ᐟ⁹ = (1/3²ᐟ⁹) = 3⁷ᐟ⁹ ⁻¹ = 3⁷ᐟ⁹/3¹ = {⁹√(3⁷)}/3 = {⁹√(2187)}/3. .
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Имею плохую привычку. Начав что то смотреть, досматриваю до конца, а потомстрадаю от потерянного времени.
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solving very bad..to long...
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Похоже, чуваку просто нравится пером по бумаге водить))) Продемонстрировал фантастическое владение степенями!
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Так мало того, сама по себе задача крайне глупая.
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Only ((3)^-2)^(1/9)=3^(-2/9)
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I have never seen such inefficiency.
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Super Academy, A bit tedious process... ( Maybe the result here is a bit easier: (1/9)^(1/9) = 1 / 9^(1/9) = 3^(-2/9) = 1/3 * 3^(7/9) = 1/3 * (3^7)^(1/9) = 1/3 * 3^(6/9) * 3^(1/9) = 1/3 * 3^(2/3) * 3^(1/9) = 1/3 * cbrt(9) * root(3; 9). Here root(a; b) means a^(1/b) for a∊ℝ, b∊ℕ, and cbrt(x) is a cube root of x∊ℝ. What is the meaning of simplification in this case? I'm from Russia, and in our high school we have no strict rules for the result of simplification.
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Herr professor, if your friend did this sea of calculations and is going to give a value that needs to be calculated using a log or calculator, wouldn't it be much simpler to use the following scheme: 1) (1/9)^(1/9) = X 2) I raise both sides to the power 9 1/9 = X^9 0.111111 = X^9 X = ninth root of 0.1111111111 It will give the same value as yours, calculated, 0.78338 Hugs!
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= ((1/3)^2)^(1/9) = (1/3)^(2/9) = 3^(-2/9) = 3^(7/9)/3 Apart from the very exercise being quite strange, the result you came across in the end of these 14 minutes can be produced in 20 seconds or so
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Chłopie, ty to skomplikowałeś, a nie uprościłeś !... przez logarytm o podstawie 3 szybko wychodzi 3^(-2/9)
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What is exactly the scholar level of students who have to solve this ? This solution is too long and if a student had to solve this during math Olympics, this would be a waste of time !!!😮
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If it is a question of Math Olympiad then everyone would succeed in that exam....even myself.
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There is a faster and less tedious method
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It doesn't make sense. You only demostrated the different ways of manipulation expression rather than simplify it.
