Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math

Middle School Archive

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

This page:
  exponents checkmark

  Dr. Math

See also the
Dr. Math FAQ:
  order of operations

Internet Library:


About Math

   factoring expressions
   graphing equations

   factoring numbers


     conic sections/
   3D and higher



Number Sense
   factoring numbers
   negative numbers
   prime numbers
   square roots

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: [<prev]  1  2  3  4 [next>]

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]

Home || The Math Library || Quick Reference || Search || Help 

© 1994-2015 Drexel University. All rights reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.The Math Forum is a research and educational enterprise of the Drexel University School of Education.