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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.

Cube Root by Hand [01/23/1998]
How do you calculate the cube root of a number without using a calculator?

Dividing Negative Exponents [10/14/1998]
Why does a negative exponent become positive when you divide by it?

Do Irrational Roots Always Occur in Conjugate Pairs? [03/13/2002]
A colleague and I have been puzzled by the equation x^3+4x^2+3x+1=0. Upon graphing, there appear to be two imaginary solutions and one real solution...

Exponents and Negative numbers [03/02/1997]
Why wouldn't the answer to -3 squared, standing alone and without parenthesis or brackets, be -9?

Heron's Method for Finding Square Roots by Hand [12/18/2001]
How do you get the square root of a number manually without a table or calculator?

Negative Exponents Explained [12/29/2001]
I have a problem with exponents like 5 to the negative second.

Negative Square Roots on Calculators [10/30/1995]
Every time I try to calculate on my calculator the square root of a negative number (-4, for example) I get the message "Error". Why?

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?

Proof that Sqrt(2) is Irrational [8/29/1996]
What is the proof that the square root of 2 is irrational? I recall it begins with the assumption that sqrt(2) is rational...

Square Root of a Negative Number [01/25/1997]
Is it possible to find the square root of a negative number and, if so, to what number system do these square roots belong?

Why Simplify Square Roots? [05/17/1999]
We have been trained to simplify square roots, but we are now looking at the reasons why we should continue to teach the process.

1005! / 10^n: A Number Puzzle [9/11/1996]
Find the largest positive integer, n, such that 1005! is divisible by 10 to the power of n.

21^100 - Last Two Digits [09/04/1997]
What are the last two digits of 21 to the 100th power?

2/3 Power using a Calculator [07/05/2001]
Can -512 be the answer to the equation x^(2/3) = 64?

2^99 Divided by 99 [08/27/2001]
What is the remainder when you divide 2^99 by 99?

Adding Square Roots [10/31/1995]
I don't understand how to add 3 Radical 81 + 2 Radical 25.

Algebra 2: Exponents [01/07/1998]
I need to find out what "x" is in this problem: x^x^3 = 3.

Algorithm for Simple Fractional Exponents [03/14/2002]
How can I explain to my program how to resolve simple fractional exponents using only addition, subtraction, multiplication, division, square, and square root?

Alternative Formulas for Growth and Decay [08/02/2002]
I have two formulas for growth and decay: q = q_0*e^(rt), and q = q_0*a^t. What is the difference between them?

Applications of Non-antidifferentiable Functions [01/29/1999]
What are some of the real life applications of the functions sin (x)/ x, e^(-x^2), and sin (x^2)?

Approaching Zero and Losing the Plot [11/11/2010]
Looking near the origin at plots of y = x^n for ever tinier n, a student wonders why y = x^0 does not equal zero. By emphasizing two different limits, Doctor Ali gets the student back into line -- specifically, y = 1.

Are Exponents Associative? [02/05/2002]
How much is 2^(i) or x^(i) ?

Are Negative Exponents Like Other Exponents? [08/21/2002]
Is there a general rule for doing all exponents, or does a negative exponent have nothing in common with positive exponents?

Arithmetic vs. Exponential Increases [05/06/1999]
What does "....the work produced... will increase exponentially rather than arithmetically" mean?

Base e, In, Log [03/08/2002]
Problems in base e. For example: 3e^(2x-1) = 7, or e^(x+1) = 8.

Base of an Exponential Function [09/15/2001]
Why can't the base of an exponential function be negative?

Binary Exponentiation [09/13/2001]
Show how to compute 5^21 using 6 multiplications. How many multiplications are needed to compute 7^7024?

Calculate the Derivative for Sqrt(x^5) [03/09/2003]
Why does the calculator fail when I calculate the derivative for sqrt(x^5)?

Coal Consumption [01/13/1997]
How long will coal reserves last if consumption increase at the rate of 3.1 percent per year?

Code with Only a String of 1's [10/28/2002]
You need to send a numeric code to someone, such as one used to unlock a padlock.

Combining Positive and Negative Exponents [06/30/1999]
When you simplify exponential expressions using the power rule, how do you combine positive and negative exponents in the numerator and denominator?

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?

Complex Exponentiation [02/20/2015]
A teen struggles to evaluate expressions with complex numbers in their exponents. Using De Moivre's Theorem and polar coordinates, Doctors Ali and Peterson break down the method.

Complex Radicals [11/27/2001]
I understand the square root, but how do you use the cubed root?

Conjugates with Square Roots [1/29/1996]
I don't understand what conjugates are in relation to square roots, and what good they do.

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?

Cubic Equations [01/19/1998]
How would you solve a problem like 3x^3+x^2+15x+27 = 0?

Cubic Equations in One Formula [11/27/2001]
I know the formula for solving quadratic equations of the type ax^2+bx+c=0, but is there a formula for cubic equations?

Cubic Functions [10/15/1997]
How do I solve a cubic equation like f(x) = x^3-2x^2+4x-5 ?

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