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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 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(cx)) + 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 ThirdDegree 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 512i.
 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 (1^31^2)+(2^32^2)+(3^33^2)... (15^315^
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 OwensWendt 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.
 Unnesting 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  (2c3)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 noninteger
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.
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