Ask Dr. Math

Middle School Archive

Browse Middle School Exponents
Stars indicate particularly interesting answers or good places to begin browsing.

Selected answers to common questions:
    Negative exponents.
    Scientific notation.

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Dividing Negative Exponents [10/14/1998]

Why does a negative exponent become positive when you divide by it?

Explaining Exponents [10/23/1997]

I do not understand how to solve exponents.

Explaining Scientific Notation [10/21/2002]

Could you try to explain scientific notation to me?

Exponents [12/04/1996]

I have trouble working out exponent problems. Is there an easy way to work them or understand them?

Exponents and Negative numbers [03/02/1997]

Why wouldn't the answer to -3 squared, standing alone and without parenthesis or brackets, be -9?

Exponents in the Real World [11/23/1997]

How come we have to know how to add, subtract, multiply, and divide exponents? When do you add them?

Fractional Exponents [08/09/1997]

Is there a proof for X^1/2 = the square root of X?

Multiplying by a Power of Ten [10/31/2001]

Give the power of ten that the decimal must be multiplied by to eliminate the decimal point in the numbers: 3.825; 6.91; 19.207.

Negative Exponents Explained [12/29/2001]

I have a problem with exponents like 5 to the negative second.

Properties of Exponents [01/22/2001]

Will you please help me understand exponents?

Question about Exponents [11/9/1994]

(2x^2 y^3)^4(-x y^2)^2 = ?

Scientific Notation [01/16/1997]

Writing very large or very small numbers.

Scientific Notation [03/06/1997]

I'm having a hard time writing 32,500,000,000 in scientific notation.

Scientific Notation [08/19/1997]

Write these numbers in scientific notation: 55000, 0.55, x...

Scientific Notation: Exponents [8/29/1996]

What do you call 0.000000000000000000000002?

Scientific Notation, Standard Form [03/14/1997]

Write 5.2 x 10^6 in standard form.

Square Root of a Negative Number [01/25/1997]

Is it possible to find the square root of a negative number and, if so, to what number system do these square roots belong?

What is an exponent? [8/8/1996]

Can you explain what an exponent is?

Zero as an Exponent [7/15/1996]

Why does n^0 = 1?

Zero as an Exponent [2/1/1996]

2^3 is 2 times itself 3 times or 2x2x2. But 2^0 isn't 2 times itself 0 times, is it? Can you explain 2^0 in those terms?

Zero to the Zero Power [9/6/1995]

Since anything to the zero power is always one, then what is the correct solution to what zero to the zero power is?

0.000001 to the Ninety-ninth Power Times Itself [05/19/1999]

We want to know what 0.000001 to the ninety-ninth power times 0.000001 to the ninety-ninth power is.

0 Power [8/4/1996]

Why is any number to the 0 power equal to one?

1005! / 10^n: A Number Puzzle [9/11/1996]

Find the largest positive integer, n, such that 1005! is divisible by 10 to the power of n.

21^100 - Last Two Digits [09/04/1997]

What are the last two digits of 21 to the 100th power?

2/3 Power using a Calculator [07/05/2001]

Can -512 be the answer to the equation x^(2/3) = 64?

7 to the 1997th power [09/22/1997]

How would you find what the 1997th power of 7 is?

Adding and Subtracting Radicals [03/08/2001]

How can I simplify expressions with radicals in them?

Algebra and Exponents: -4^2 = ? [06/30/1998]

I had an argument with a professor over this topic. I say 16, he says - 16.

Anything to the 0 Power [11/21/1997]

Why is anything to the 0 power 1?

Arithmetic vs. Exponential Increases [05/06/1999]

What does "....the work produced... will increase exponentially rather than arithmetically" mean?

Arranging Numbers by Order of Magnitude [3/25/1996]

Starting with the smallest, arrange the following numbers in increasing order of magnitude: 6^200, 5^300, 4^400, 3^500, 2^600

Calculators and e+ [09/27/1998]

What does the "e+" mean on a calculator?

Code with Only a String of 1's [10/28/2002]

You need to send a numeric code to someone, such as one used to unlock a padlock.

Combining Positive and Negative Exponents [06/30/1999]

When you simplify exponential expressions using the power rule, how do you combine positive and negative exponents in the numerator and denominator?

Decimal Exponents [03/19/1999]

Find x^y, where y is a decimal, without using a calculator.

Decimal Exponents [11/07/2001]

Can you have exponents that are decimals?

Defining Powers of Ten [09/22/2004]

Is a power of 10 always the product of a certain number of 10s, or can 1/10 and 1/100 also be considered powers of 10?

Dividing with Powers [01/16/2003]

I am having trouble with problems like (6.0 * 10^7)/(3.0 * 10^2).

Doubling Bacteria [09/17/1997]

How many bacteria are in the colony?

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