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 TOPICS This page:   exponents    Search   Dr. Math See also the Dr. Math FAQ:   order of operations Internet Library:   exponents/roots MIDDLE SCHOOL About Math Algebra    equations    factoring expressions    graphing equations Arithmetic    division    exponents    factorials    factoring numbers    fractions/percents    logarithms Definitions Geometry    2-dimensional      conic sections/        circles      triangles/polygons    3D and higher      polyhedra History/Biography Logic Measurement    calendars/      dates/time    temperature    terms/units Number Sense    factoring numbers    negative numbers    pi    prime numbers    square roots Probability Puzzles Ratio/Proportion Statistics Word Problems Browse Middle School Exponents Stars indicate particularly interesting answers or good places to begin browsing. Selected answers to common questions:     Negative exponents.     Scientific notation. 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 past? 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 power. 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 polynomials? 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 only once. Page: []

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