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Browse College Exponents

Stars indicate particularly interesting answers or good places to begin browsing.



Palindromic Squares [07/28/1997]
Do you know any numbers besides 14641 where both the number and its square root read the same left to right as right to left?

A Way to Express i to the i [4/17/1995]
I know e to the iA = cosA + i sinA, where iA is the exponent. Is there another way to express i to the i?

Comparing n^k and k^n [04/03/2007]
If n > k, which is greater, n^k or k^n? Is there any general rule to fit this situation?

Comparing Numbers With Huge Exponents [05/23/2002]
Which is larger, 1999^1999 or 2000^1998?

The Constants pi, e, i, 0, and 1. [6/28/1995]
A friend told me that e^(pi*i) = -1. (That is, e to the power of pi times i equals negative one.) Can you tell me anything about this?

Cube Roots of Numbers [11/05/1997]
If you take i (sqrt(-1)), the cube root is -i, but since x^3 = i is degree three there should be three different values of x. What are they?

Exp, Log, and Ln Functions Explained [7/31/1996]
What is the exp function? When is it needed? Also, how do I calculate Log and Ln functions with basic arithmetic and logic?

Exponential Decay [06/09/2005]
Does an exponential decay calculation ever reach zero?

Exponent Math Puzzle [07/09/2006]
What is the remainder when 3^4^5^6^7... to infinity is divided by 17?

Finding Roots of Polynomials with Complex Numbers [09/27/2001]
I read in the archives that you can find the roots of 3rd or higher- degree polynomials with complex numbers...

How Many Digits in 13^18 ? [05/15/2003]
Finding the exact number of digits in 13 raised to the 18th power, with and without a calculator.

Inverses within Semigroups [05/06/2002]
I would like to know the value of e in a semigroup for exponentiation, if it exists. In other words what CONSTANT value e satisfies the equation, a^b = e?

The ith Root of -1 [09/16/1999]
Why does the ith root of -1 equal 23.14069...?

Pell-like Diophantine Equations [10/05/2010]
How do you solve exponential Diophantine equations in two variables? Even after seeing recurrence relations and modular arithmetic simplify his original problem, a student remains curious about additional strategies, so Doctor Vogler obliges by outlining more advanced methods.

Pi-th Root of -1 [12/15/2000]
How can you find the pi-th root of -1?

Proving a^x = a^y iff x = y [12/13/2000]
How can I prove that a^x = a^y iff y = x for all real numbers x and y?

Which is Greater? [2/12/1996]
Let be A = 10001^9999 and B = 10000^10000. Which is greater? Why?

Why Is (-n)^fractional Invalid ? [05/26/2003]
The problem is with negative numbers being raised to a fractional exponent.

y to the x Power [06/10/2003]
How can I calculate the real and imaginary parts of any non-integer powers of negative numbers?

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