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Selected answers to common questions:
- Simplifying with Cube Roots [01/22/1997]
Simplify: cube root(3) / [cube root(6) + cube root(3)]
- Simplify the Expression [08/21/1997]
... and eliminate any negative exponents: (4b)^1/2(8b^2/5).
- Smaller vs. Larger Exponents and Numbers [03/24/2003]
Is a smaller number with a large exponent greater than a larger
number with a smaller exponent?
- Solve for x: 131,072 = 2^x [09/12/2001]
How do I solve the following equation for x: 131,072 = 2^x? I know the
answer is 17, but can't remember how to solve it.
- Solve for X Algebraically [07/24/2003]
Solve for x algebraically, (no graphing): 2^x + 2^(-x) = 5.
- Solving an Equation with Sines and Exponents [05/24/2000]
How can I solve the equation sin^2(exp(c-x)) + sin^2(exp(c+x)) = 0, where
x is a (real) unknown and c is a real positive constant?
- Solving Radical Expressions [07/26/1998]
How do you solve radical expressions such as the cube root of 32 minus
the cube root of 108?
- Solving Third-Degree Equations [09/24/2001]
I'm trying to solve x^3 + 2x^2 - 3x - 4 = 0. I need to take the square
root of 4p^3 + 27q^2, which is -272. I'm looking for the real solutions,
and there are three of them.
- Speed of Light [06/08/2001]
What's m s^-1? Why isn't it just m/s (meters per second) instead? What's
the little "-1" at the end?
- Sqrt2 Irrational [05/17/1999]
How do you prove that the square root of 2 (or other roots of other real
numbers) is irrational?
- Square Root of 3 [05/18/1999]
How can I prove that the square root of 3 is an irrational number?
- Square root of a complex number. [6/6/1996]
Find the square root of 5+12i. (Let the square root of 5+12i = a+bi.)
- Square Roots in Binary [10/03/2000]
Can you show an example of taking the square root of a binary number?
- Square Roots Of Complex Numbers [02/22/1999]
Find the square roots of 5-12i.
- Square Roots using Basic Arithmatic [03/19/2002]
Given X and Y, solve for Z using only basic operations: X = Z^Y; X = 729,
Y = 6.
- Square Root Trick [08/13/1997]
Is there a formula to calculate sqrt(x+sqrt(x+sqrt(x+... ?
- Srinivasa Ramanujan [03/28/1999]
What are the mathematical contributions of Srinivasa Ramanujan?
- Straight Line on the Graph [09/10/1998]
Let f(x) = ae^(kx) where a>0 and k are constants. Show that the graph of
y = ln(f(x)) is a straight line.
- Summing Exponents [06/11/2002]
If you multiply successive powers of 3 (i.e., 3^1 * 3^2 * ...) to get
3^210, what is the final power of 3 in the list?
- Sum of First n Cubes, First n Squares [11/18/2002]
Is there a shortcut to find (1^3-1^2)+(2^3-2^2)+(3^3-3^2)... (15^3-15^
- Surds [05/17/2000]
Where does the term "surd" for square roots come from?
- Theorem About Sum and Product of Quadratic Roots [03/07/1998]
Explain why 1/2 and 3/4 are NOT the roots of 0 = 4x^2 + 5x + 8.
- Two New Variables [10/25/2002]
I am trying to calculate using the Owens-Wendt equation. The equation
will give two equations with two unknowns. I am unable to solve
them, because of the x^1/2 and y^1/2 powers.
- Un-nesting Radicals [03/16/2001]
How can I simplify sqrt(2+sqrt)?
- Using Mod to Find Digits in Large Numbers [12/10/1996]
Find the last two digits in 1996^1996.
- Using the Distributive Property [03/06/2002]
This question is actually from my chemistry class: -2.4222 x 10^-19 - (-
6.0556 x 10^-20).
- What is i^(Googol)? [05/27/2000]
What is the value of i raised to the googol power?
- When FOIL Fails [03/22/2001]
Find the product - (2c-3)3rd power. I can do FOIL on a question to the
second power, but I cannot figure out how to do a question to the third
- Why Cubed? [11/27/2001]
Why do we use "cubed" for the volume of a figure?
- Why does ln(-x) x>0 equal ln(x)+pi*i? [6/5/1996]
Could you please explain why the ln(-x) x>0 equals ln(x)+pi*i?
- Why Is an Exponent of 1/2 the Same as a Square Root? [05/05/2004]
Why is raising a number to the 1/2 power the same as taking the square
root of the number? For example, 36^(1/2) = 6.
- Why Is (-n)^fractional Invalid ? [05/26/2003]
The problem is with negative numbers being raised to a fractional
- Why Multiple Roots? [9/9/1996]
Why does raising an equation to an even power introduce an extraneous
- x^x, Discrepantly [12/04/2013]
Calculators evaluate x^x differently for small positive values of x. Piecing together
clues about equivalent fractions, decimals, and degree measures, Doctor Peterson
gets to the roots of the discrepancies.
- 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?
- Zero as an Exponent [7/15/1996]
Why does n^0 = 1?
- The Zero Power of Two [12/10/1998]
Why is 2 to the 0 power equal to 1? I don't understand how a number can
be multiplied by itself zero times.
- Zero to a Negative Exponent [05/06/2001]
Is 0^(-3) equal to 0, or is it undefined? We can't determine whether to
use the 0^x = 0 rule, or to interpret it as 1/(0^3).