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Browse High School Exponents
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Negative exponents.
    Scientific notation.

Simplifying Radicals [06/18/2001]
In the following: sin(15) = sqrt(2-sqrt(3))/2 = (sqrt(6)-sqrt(2))/4, how do you manipulate sqrt(2-sqrt(3))/2 to obtain (sqrt(6)-sqrt(2))/4?

Simplifying Radicals and Exponents [9/3/1995]
A student asks how to simplify square roots and numbers with exponents.

Simplifying Square Roots [9/5/1995]
Could you help me with this problem? 1/2 *Sqrt{24}

Simplifying the Square Root of a Sum [09/27/2004]
Why is it that sqrt(a + b) does not equal sqrt(a) + sqrt(b)?

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^ 2)?

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[3])?

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 power.

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 exponent.

Why Multiple Roots? [9/9/1996]
Why does raising an equation to an even power introduce an extraneous root?

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?

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