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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 Nonantidifferentiable 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^(2x1) = 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^32x^2+4x5 ?
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