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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?

Parsing Powers Raised to Powers [11/13/2016]
An adolescent seeks the order of operations for evaluating stacked exponentiation. Doctor Peterson shares the conventional interpretation.

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.

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