Ask Dr. Math Middle School Archive

Dr. Math Home || Elementary || Middle School || High School || College || Dr. Math FAQ

 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. Number of Ancestors 1000 Years Ago [11/22/1999] How many living relatives would I have had 1,000 years ago, assuming 25 years per generation? Numbers Expressed as Exponents [08/27/1997] How do you express .0000025 and 758,000,000,000 using an exponent? Numbers with Large Exponents [08/22/2001] How many zeros end the number 2^300 * 5^600 * 4^400? Ones Digit of 3^100 [08/18/1999] What is the number in the ones place of the value of 3^100? How can you find it without multiplying 3 one hundred times? Operations in Scientific Notation [08/30/2001] How do you add, multiply, and divide in scientific notation? Ordering the Operations [11/10/1998] Why does the order of operations have to be in that order? Who set that specific order of operations? Perfect Square: Definition [10/24/1999] What is a perfect square? Positive and Negative Exponents [07/27/1997] Why does (-1)^n = 1 for any even number n, and why is (-17) ^-8 positive? Power of 120 [06/12/2001] Is there a quick way to work out 1.05 to the power of 120? Power or Exponent? [10/14/2003] I always thought that 'power' was just a synonym for 'exponent'. Is that incorrect? Powers [10/7/1996] What is it called when you have a number with a superscript of another number? The Purpose of Powers [07/30/2002] I don't understand the purpose of powers, what they do, and how to use them. Raising a Power to a Power [11/27/1997] Why isn't [(-x)to the 5 power]to the 8 power -x? Raising Both Sides of an Inequality to a Power [06/19/2006] You have to flip the sign in an inequality if you multiply both sides by a negative number. Is there any rule that says when you have to flip the sign if you raise both sides to a power? Rules of Exponent Manipulation [1/22/1996] f sub r equals the reciprocal of ... Scientific Notation [09/16/1997] I don't understand how you get the answer: 5x10 to the 3rd power = 5,000; 5x10 to the -3rd power = -5,000. Scientific Notation and Engineering Notation [10/10/2001] Convert 0.000 000 000 000 000 000 000 3 to: a) scientific notation; b) engineering notation. Shortcut for Computing x^n [07/05/2002] Is there a shortcut that can be used to compute values like 3^12, without doing 12 separate multiplications? Significant Digits in Measurement [08/13/2001] I understand that there are rules to determine the significant digits in measurement, but aren't all digits significant, especially zeros for place value? Significant Figures and Scientific Notation [05/21/1997] How do you tell how many significant figures a number has? Simplifying Exponential Equations [08/19/2003] A review question: (3r^-1s^2t^3)^2/27r^3st^-2. I don't even know how to begin. Simplifying Expressions Using Exponent Laws. [02/08/1998] Simplify: 5 to the exponent -4/3 divided by 5 to the exponent 2/3 Simplifying the Square Root of a Sum [09/27/2004] Why is it that sqrt(a + b) does not equal sqrt(a) + sqrt(b)? Simplifying with Cube Roots [01/22/1997] Simplify: cube root(3) / [cube root(6) + cube root(3)] Smaller vs. Larger Exponents and Numbers [03/24/2003] Is a smaller number with a large exponent greater than a larger number with a smaller exponent? Solve for x: 131,072 = 2^x [09/12/2001] How do I solve the following equation for x: 131,072 = 2^x? I know the answer is 17, but can't remember how to solve it. Speed of Light [06/08/2001] What's m s^-1? Why isn't it just m/s (meters per second) instead? What's the little "-1" at the end? Srinivasa Ramanujan [03/28/1999] What are the mathematical contributions of Srinivasa Ramanujan? Straight Line on the Graph [09/10/1998] Let f(x) = ae^(kx) where a>0 and k are constants. Show that the graph of y = ln(f(x)) is a straight line. Subtracting Exponents when Dividing Like Bases [01/21/2005] I need to simplify x to the seventh power over x to the third power. I think I should divide 7 by 3 and put that as the power, but that gives me x to the 2.3 repeating power, and the book says it's x to the fourth. Surds [05/17/2000] Where does the term "surd" for square roots come from? Talking About Exponents [06/11/2002] When a number is cubed, would you say that it's multiplied by itself two times, or three? And why? The Term Power [10/23/2001] One of my students asked how we came to use the term power to express the number of times we multiply a number by itself. Understanding Exponents [10/24/1996] Can you help me understand exponents? What is 88^8? Units Digit of 2^57 [10/07/2001] What is the units digit of 2 to the power of 57? Using Mod to Find Digits in Large Numbers [12/10/1996] Find the last two digits in 1996^1996. Using Scientific Notation [11/01/1997] I know it's used to multiply large numbers to get a correct answer, but I don't understand how to do it. Value of 9^(9^9)? [10/21/2002] What is the value of 9^(9^9)? When FOIL Fails [03/22/2001] Find the product - (2c-3)3rd power. I can do FOIL on a question to the second power, but I cannot figure out how to do a question to the third power. Who Invented the Square Root? [12/11/1996] I've only seen long, stringy roots! Page: []

Search the Dr. Math Library:

 Search: entire archive just Middle School Exponents Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

[Privacy Policy] [Terms of Use]

© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/