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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...?
 Pelllike 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.
 Pith Root of 1 [12/15/2000]

How can you find the pith 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 noninteger
powers of negative numbers?
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