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High School Archive

Browse High School Exponents
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Selected answers to common questions:
    Negative exponents.
    Scientific notation.

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Decimal Exponents [03/19/1999]

Find x^y, where y is a decimal, without using a calculator.

Decimal Exponents [11/07/2001]

Can you have exponents that are decimals?

Defining Powers of Ten [09/22/2004]

Is a power of 10 always the product of a certain number of 10s, or can 1/10 and 1/100 also be considered powers of 10?

Derivation of the Equation of an Ellipse [06/23/1999]

How can I derive the equation of an ellipse from its definition?

Deriving a Formula for Cubic Roots [05/22/1998]

Is there a working formula to solve the 3 roots of a cubic? I'm trying to derive it but am having trouble...

Descartes' Square Root Method [10/30/1996]

Why does Rene Decartes' geometric method for finding square roots work?

Dividing 1005! by 10^N [9/5/1996]

Determine the largest integer N such that 1005! is divisable by 10^N.

Dividing Positive and Negative Exponents [12/18/1997]

Do I put the variables with negative exponents on the bottom?

Does (a^m)^n Always Equal a^(mn)? [09/30/2009]

Is the exponent law (a^m)^n = a^(mn) always true? Maybe not! A look at some cases where the law needs some careful interpretation.

Doubling Time [03/08/2002]

If the cost of an all-day ski lift ticket at Colorado's Vail Ski Area has been growing at about 7% per year ever since 1963, when a ticket was $5, what did it cost in 1993?

EE Key on a Calculator [10/25/1999]

What does "EE" on the calculator stand for?

E in the Modern World [01/06/1998]

I am looking for examples of how e exists in the modern world.

e^pi Greater Than pi^e [03/29/2003]

How can I show that e^pi is greater than pi^e without using a calculator?

Equation without a Solution [11/14/2001]

What is the solution to the equation sqrt(x) = -2 ?

Etymology of the Word Radical [12/28/2001]

Where does the word radical come from?

Euler Equation and DeMoivre's Theorem [05/18/1999]

Do you have a proof of the equation e^(i*Pi) + 1 = 0?

Euler's Number [01/28/1998]

Why is Euler's number referred to as the natural base?

Evaluating Large Numbers [06/11/1998]

How do you evaluate 2^71 * 3? Can you use logarithms?

Explicit Inverses [04/21/1999]

How do you solve x^x = 5 without graphing or guessing?

Exp, Log, and Ln Functions Explained [7/31/1996]

What is the exp function? When is it needed? Also, how do I calculate Log and Ln functions with basic arithmetic and logic?

Exponential Decay [05/02/1997]

After 69 days, a certain amount of Radium F had decayed to 1/sqrt(2) of its original mass. Determine the half-life of Radium F.

Exponential Decay [04/28/2003]

The English language evolves naturally so that 77% of all words disappear or are replaced every 1000 years. Of the words used by Chaucer in 1400 A.D., what percentage should we expect to find still in use today?

Exponential Decay [06/09/2005]

Does an exponential decay calculation ever reach zero?

Exponential Equations [01/19/2003]

Is there a mathmatical way to solve 2^x + 3^x = 13?

Exponential Growth in Dividing Bacteria [01/08/2004]

Suppose a bacterium divides in half an hour, then the two resulting bacteria divide in the next half an hour. At this rate, how many bacteria would there be in 72 hours?

Exponential Growth on a Family Tree [12/26/2002]

What is the probability of my being related to a famous person of the past?

Exponent Math Puzzle [07/09/2006]

What is the remainder when 3^4^5^6^7... to infinity is divided by 17?

Exponents as Variables [11/20/2001]

I can solve these problems but I don't know how to prove them: 9^1+x= 27; 2^-x-4=1/32; 243=(1/3)^x+4; 64=0.5)^3-x.

Exponents Containing Negative Integers [12/15/1998]

Order of operations and raising a negative number to a power.

Exponents on a Scientific Calculator [08/21/1997]

My problem is that I am not using the EXP key correctly...

Extraneous Roots [06/13/2001]

The solution 4 (to sqrt(x-3) = x-5) only works for a negative root; 7 only works for a positive root. Which solution is valid?

Factoring: Difference of Cubes [09/05/2001]

Factor a^3b^3 - 8x^6y^9.

Finding 13^99 [11/21/2001]

What is the units digit of 13 to the 99th power?

Finding a Decimal Exponent [03/21/1998]

How do you find 32^0.4 without using a calculator?

Finding Roots of Polynomials with Complex Numbers [09/27/2001]

I read in the archives that you can find the roots of 3rd or higher- degree polynomials with complex numbers...

Finding Roots on a Calculator [04/22/2001]

How can I use the equation HPR = (1.667)^(1/5) on a calculator that does not have a fifth root key?

Finite vs. Rational [9/10/1996]

A right triangle with sides 1 and 2 has a hypotenuse equal to the square root of 5, which is irrational - it carries on to infinity without recurring - but the side length of a triangle must be finite!

Formula for Finding Mth Root [08/16/2001]

I read your article about finding square roots without using a calculator. Is there also a formula for finding cube roots, fourth roots and so on?

Four Methods for Extracting Cube Roots [03/03/1998]

Extracting cube roots by factoring, calculator, guess and check, and iteration.

Fractional Bases in Exponential and Logarithmic Functions [04/06/2009]

In the equation log_a(x) = a^x, can the base be a fraction? Doctor Ali introduces a student to the Newton-Raphson Method and LambertW function.

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