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 TOPICS This page:   exponents    Search   Dr. Math See also the Internet Library:   exponents/roots HIGH SCHOOL About Math Analysis Algebra    basic algebra    equations/graphs/      translations    linear algebra    linear equations    polynomials Calculus Complex Numbers Calculators/    Computers Definitions Discrete Math    permutations/    combinations Exponents    Logarithms Fibonacci Sequence/   Golden Ratio Fractals Functions Geometry    Euclidean/plane      conic sections/        circles      constructions      coordinate plane      triangles/polygons    higher-dimensional      polyhedra    non-Euclidean    practical geometry    symmetry/tessellations History/Biography Interest Logic Negative Numbers Number Theory Physics/Chemistry Probability Projects Puzzles Sequences/Series Sets Square/Cube Roots Statistics Transcendental   Numbers Trigonometry Browse High School Exponents Stars indicate particularly interesting answers or good places to begin browsing. Selected answers to common questions:     Negative exponents.     Scientific notation. 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. Fractional Exponents [03/11/1999] I am trying to figure out the water consumption of the average goat. Fractional Exponents [12/07/2003] When a number is raised to a power like 4/3 or 3/5, how is it done? Functionality of the Square Root [4/27/1996] I maintain that the relation indicated by the statement: SQRT(x) = 3D y (limited to real numbers) is a function, whereas my teacher claims it is not. Graphing y = (-2)^x [05/27/2005] How do I graph y = (-2)^x, or any function where you have a negative number raised to a power? Graph of y = (-n)^x [01/17/2005] I am curious as to what the graph of y = (-n)^(x) would look like, such as y = (-2)^x. My graphing calculator will not show the graph as anything, but displays many real values in the table of values. Half Life of Money [04/13/2001] What is the standard accepted formula for determining the amount of time it takes for money to lose half of its value due to inflation? I've found two, they are: t = t = log2/r and t = log2/log(1+r). 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? How Do Cube Roots Work? [11/04/2003] I understand square roots but I'm not sure how to do cube roots. Can you help? How Many Digits in 13^18 ? [05/15/2003] Finding the exact number of digits in 13 raised to the 18th power, with and without a calculator. i and (-1) with Multiple Powers [08/09/2001] What is the order in which i and (-1) should be raised when using multiple powers? Why is it possible to obtain so many different values? Importance of Linear Functions [02/06/2002] What is the importance of linear functions in the real world, and how are they used? Indirect Proof [02/14/1998] Prove that sqrt(2) is an irrational number. Integral of Ln x [3/31/1996] What is the integral of the natural log of x (ln x)? Interpreting 2^3^2 [04/26/2001] Why is 2^3^2 interpreted as 2^(3^2) = 512 instead of (2^3)^2 = 64? An Introduction to Exponential Growth [10/07/2006] What exactly is exponential growth? I see an equation in my book, but I'm not sure what it means or how it works. Investigation Involving Square Root of 2 [07/09/2001] How can you explain the fact that (665857/470832)^2 = 2? Is Doubling Exponential? [7/17/1995] The amount of information storable in silicon has roughly doubled every year. Many authors have written articles about this "exponential growth rate." Is doubling exponential? (i)th Root and (i)th Power [02/13/1999] How do you simplify x to the power of i (and 1/i), where x could be any number? 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? Limits Approaching Infinity [02/16/2002] Is the only way to answer them by memorizing all the general questions you may come across? 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? Logarithmic Equivalent of the Inverse Hybolic Cosine Function [10/28/1997] I recently attempted a question which I think I have done wrong and I was wondering if there were a set formula for this problem... Log Problem [5/5/1995] Solve: 3(3^x)+9(3^-x) = 28. Logs in Different Bases [6/11/1996] Solving equations with different base logs. Logs with Different Bases [11/26/1997] How do you do an addition problem involving logs with different bases? Manually Calculating Logs and Exponents [12/16/2001] Can you give me a formula to calculate base 10 logarithms and exponents? Modular Arithmetic and Finding a 13th Root [11/29/2004] A discussion of a method for easily finding 13th roots based on modular arithmetic. 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 Square Roots of Negative Numbers [11/25/2003] It seems to me there are two possible ways to interpret a problem like sqrt(-2) * sqrt(-2). One way I get 2 and the other way I get -2. Which solution is correct? What's wrong with the other one? 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 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 Numbers to Powers [11/23/2001] If u is an irrational number and x is a negative number, what is x^u? How do I determine even whether that number is positive or negative? Nested Negative Exponents [8/2/1996] How do I deal with nested negative exponents? Nested Radical [02/25/2002] Prove the following nested radical: sqrt(1+2sqrt(1+3sqrt(1+4sqrt(1+...)))) = 3 Page: []

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