See also the
Dr. Math FAQ:
order of operations
3D and higher
Browse Middle School Exponents
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
- Easier Way to Evaluate Powers [9/7/1996]
Is there an easy way to evaluate an exponent like 7 to the 9th power?
- EE Key on a Calculator [10/25/1999]
What does "EE" on the calculator stand for?
- Exponent Divided by Another Exponent [9/8/1996]
How do I solve (8^7)/(8^3)?
- 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
- Exponent of Negative Integer [07/27/1997]
We are having a debate about the value of -5^2 (neg five squared).
- 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...
- Exponent zero = 1; pi [12/3/1994]
I am a grade 9 math teacher in the Yukon. I have a class that wants to
know why any number with exponent zero is equal to one. Is there an
explanation? Also, how many decimal places has pi been calculated to, and
are there any patterns emerging?
- Finding The GCF and LCM of Terms with Variables [08/25/1999]
How do you multiply terms with variables that have exponents? How can you
find the GCF or LCM of such terms?
- Finding the Units Digit [02/26/2003]
Find the units digit of 2003 to the 2003 power.
- Find X [01/22/2001]
Use your knowledge of powers and the properties of exponents to find the
value of x in the equation 8^x+2=2.
- 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!
- Five to the Third Power [09/20/2001]
What is 5 to the 3rd power? I put 15. Wrong!
- Fractional exponents [6/16/1996]
How would you go about solving (-64)^ (2/3)?
- Fractional Exponents [12/07/2003]
When a number is raised to a power like 4/3 or 3/5, how is it done?
- Fractions and Lowest Terms [07/19/2001]
Simplifying expressions: how do you finish cancelling fractions, and then
what do you multiply? What is the lowest term?
- Fractions with Exponents [01/29/2001]
I need help with questions like (-3x^2 y^2)^-2/(xyz)^-2.
- Hard Powers [12/11/1997]
We have a challenge in our math class: nine to the ninth to the ninth
- History of Exponent Notation [11/03/2003]
Why is the symbol for exponents a smaller number above the base? How
did it become this? What is the history of it?
- History of the Radical Sign [04/17/1997]
Who invented the radical sign?
- History of the Word 'Exponent' [11/26/2003]
Who came up with the name 'exponent'?
- How Can a Number Raised to the Zero Power Be One? [01/23/2008]
I know that 3^7 * 3^0 is 3^(7+0) or 3^7. That means that 3^0 must have
a value of 1. But how is that possible?
- Introduction to Linear and Exponential Growth [11/04/2003]
A population of beetles increases from 5 to 15 after one month. How
many beetles will there be after 4 months if the population is
increasing linearly? What if it's increasing exponentially?
- Last Digits and High Exponents [09/26/1998]
Calculate the following expressions without a calculator: 3^1000 and 7^
134. In each, what is the final digit?
- LCD, LCM [08/16/1997]
What is the easiest way to find the least common denominator and least
common multiple of two numbers?
- Limits to Paper Folding [05/09/2002]
What is the limit to the number of times that a piece of paper can
be folded, and how is it established?
- The Meaning of Powers, such as Squares and Cubes [3/14/1996]
What does the power mean? Like 5 to the power of 2?
- More on Why n^0 = 1 [11/03/2007]
If 2^3=2*2*2, 2^2=2*2, and 2^1=2, shouldn't 2^0= __ or nothing,
meaning that 2^0=0?
- Multiplication of Powered Numbers [02/17/1999]
What is the product of two numbers with different powers, and how many
zeros are there at the end of the product?
- Multiplying Numbers Written in Scientific Notation [06/27/2004]
How do I multiply two numbers that are written in scientific notation?
- n^0 Power = 1: Defined or Proved? [04/18/2003]
I have been wondering if a^0 is DEFINED to be 1 or is PROVED to be 1.
- Negative Exponents [9/27/1995]
What does the negative power of 2 mean?
- Negative Exponents: Who Needs Them? [09/19/2011]
A student wonders about the utility of negative exponents. Doctor Peterson elaborates
on several instances when they come in convenient.
- Negative Fraction Exponents [01/27/1999]
Can you help me simplify terms with negative fraction exponents? For
example, [2n^(1/3) - 4n^(-2/3)]/[2n^(-2/3)].
- Negative Numbers Combined with Exponentials [03/09/2001]
Why in the order of operations is negation a multiplication done after
exponentiation, rather than as a part of the base? What about
- Negative Signs in Exponents [12/2/1995]
Is (-2^2)^3 greater than or less than 2^5?
- Nested Negative Exponents [8/2/1996]
How do I deal with nested negative exponents?
- Non-integer Powers and Exponents [01/06/1999]
How do you find x^n, where n can be an integer, a fraction, a decimal, or
an irrational number?
- Number and Its Square Using All 9 Digits Exactly Once [05/22/1998]
Using multiplication facts to find all the whole numbers for which the
number and its square together use exactly nine digits 1, 2, 3, ..., 9