# powers

1. ### On process, and on the derivatives of the powers of sine

Some background: A few months ago, I was on holiday in Prague. And I saw a nice clock there. Which led me to think about the equation of time. Which led me to think about y = x + e\,\sin y Which led me to think about \frac{e^k}{k!} \frac{\partial^{k-1}}{\partial x^{k-1}} [\sin^k x] Which...
2. ### Close powers of integers

Do there exist powers of integer pairs, both greater than three, whose differences are greater than two and singly sequential? For differences zero to two: 1^N-1^N=0...3^2-2^3=1...3^3-5^2=2... ?
3. ### Sum of Powers of Primes

Maybe, it's recreational mathematics. However, is it possible to say anything about existence? Search For Numbers: Puzzle 1: Sum of Powers of Primes
4. ### Fermat's last with inverse powers

Does a^(x^-1) + b^(x^-1) = c^(x^-1) hold true for any integers {a, b, c, x}>1 where "a" does not equal "b"?
5. ### Equation with fractional powers

Hi, I'm a bit scratchy with one of the last part as you can see underlined in purple with W^2/3 = 6 & W^2/3 = -1 ... not sure whether to cube root it somehow... am just stuck. The answer is in red at the bottom. Need clarification on the steps I took, and why I got stuck, and why the answer is...
6. ### Expand in increasing powers of y-1: (1+3y-1)3

Hello :) I am stuck on this question, if anyone has any ideas that would be awesome: Expand in increasing powers of y-1: (1+3y-1)3 Thank you!! Louise
7. ### Summation of powers of powers

I have recently been asked to create a formula for the summation between 1 and N for 2^A^X where A is a given number and X is the variable. After attempting to approach this via various methods, I found that it end up simplifying to 2^A (1 + 2^A (1 + 2^AxA (1 + 2^AxAxA ... which suggests that...
8. ### Counting the number of powers

A power is defined as number n >0 power to k with k>=2 P(10)=4 (1,4,8,9) P(10^50)=? P() represents the counting function of powers.
9. ### Fraction & Powers

Hello, I've spent over an hour trying to solve this simple problem, can anyone help me, please? I have to do this without a calculator. 2^(5/2)-2^(3/2) So, both 2's cancel out so it's 2^5 - 2^3. Then it's âˆš27 - âˆš8. How do I do this part now without a calculator?
10. ### Prime-Generating Algorithm with Powers of Two?

I was doing something, when I noticed the number 256. It's a nice number. It's a power of two, and it's used in computer science a lot. Out of curiosity I added up the digits... 11. It's a prime! That got me thinking... I added up the digits of 32 which resulted in 5. Another prime! So I started...
11. ### Algebra with powers and roots?

Hello Forum! First of all, I would like to say that I'm completely new here :) I'm Danny, 22 and have been a huge maths geek since I was young. I found the following puzzle on youtube (click here if you're interested) and realised however, i have no understanding how to work with powers...
12. ### Formulas for Lowering Powers

Nevermind. Sometimes, we can have brain farts. We can get caught up in the advanced parts of math that the simple stuff can sometimes throw us off.
13. ### Help me prove this strict inequality with powers of 10

I'm trying to prove this for an exercise in my Elementary Number Theory textbook: \forall a \in \mathbb{N}: a = \sum_{i=1}^n a_{n-i}\times10^{n-i} \quad a_{n-i} \in \{0,1,2,3,4,5,6,7,8,9\} \Rightarrow a \lt 10^n I can see why it's true and I think I have the elements for the proof, but...
14. ### complex powers

Calculate ( minus ( 2 over 3 ) + ( 2 over 3 ) i ) to the power minus 4, simplifying your answer and giving it in the form a + i b, with a and b given exactly.
15. ### What does it mean to take positive rational numbers to whole-number powers?

Could you please show some examples
16. ### A question about powers

Does anyone know if there are any proofs about how close a power of 2 and a power of 3 can be? 4-3 = 1, 9-8 = 1, 32-27 = 5, 256-243 = 13... Is it safe to assume that there isn't another point at which 2^n +/- 1 = 3^n or not?
17. ### How do you take positive rational numbers to whole-number powers

How do you take positive rational numbers to whole-number powers. could you please give me some examples ? Thanks
18. ### Sum of powers of Prime numbers

\LARGE{\sum_{i=0}^{2n} p^i} is square for some n \in \mathbb{N}. Find all prime p.
19. ### (a^p)-(b^p)-(c^p) congruent to 0 (mod p) (with mild restrictive conditions)

Hello there, I recently found out about a very interesting relationship in number theory: Given a = b + c where a, b and c are integers, it is true that: (a^p)-(b^p)-(c^p) is congruent to 0, modulo p, for any prime p. *Note that this relationship is a general version of Fermat's...
20. ### Fractions! With powers! Or equations with powers and a number

I have knowledge of solving fractions without powers, e.g. (2x+2)/3+x/5=10. But for (2x(x+1))/2=20, I got to 2x^2+2x=40, what do I do next?