7.1+Negative+Exponents

Section 7.1 - Negative Exponents

 * A Quick Review of Exponents**

An exponent means you multiply the base, by itself, as many times as the exponent says. If the base is negative, the exponent does not affect the negative sign unless it is within parentheses.

So, an exponent doesn't really make a number positive or negative -- it is the base that does that, or the sign on the base.


 * Negative Exponents**

There is such a thing as a negative exponent - an exponent with a negative sign on the exponent. It is not negative, it does not make the base negative. It doesn't really have anything to do with negative.

I interpret the minus sign as "one over" or "one divided by".

A negative exponent signifies a very small number, but whether it is negative or not, depends on the sign on the base.


 * Scientific Notation**

Scientists need to use phenomenally large, and extremely small numbers. How heavy is Neptune? About 102,430,000,000,000,000,000,000,000 kilograms. In order to shorten, and simplify such large numbers, we have something called scientific notation. It uses exponents with a base of 10 to take advantage of our place value system. It uses positive exponents for large numbers and negative exponents for small numbers.

If you have a base of 10 and raise it to the third power, (10 to the third), that means 10 X 10 X 10 = 1000. Notice that an exponent of three results in three zeroes--the same number of zeroes as the exponent. We also know that if you multiply a decimal number by a power of ten, you would move the decimal the same number of spots as there are zeroes. 56.781 X 100 = 5678.1

Scientific notation looks like this: There are several rules that specify how scientific notation is written.

1. The number always starts with a single digit (1-9). 2. That first digit is followed by the decimal point. 3. Any other significant digits are included. 4. X is used to mean multiply. 5. The base is always 10. 6. A positive exponent means multiply (large number). A negative exponent means divide (small number).

To write a number in scientific notation, move the decimal so that it is immediately after the first non-zero digit. The exponent will be the number of spaces that you moved the decimal. Rather than memorize whether you move it right or left, think of the rule above -- use a positive exponent for a large number, a negative exponent for a small (less than 1) number.


 * Chapter Seven Practice Problems**

**Where to from here?**
7.1 Negative Exponents 7.2 Product Rule 7.3 Power Rule 7.4 Quotient Rule 7.5 Defining Polynomials 7.6 Adding Polynomials 7.7 Subtracting Polynomials 7.8 Multiplying Polynomials 7.9 Dividing Polynomials Chapter Seven Summary Chapter Seven Homework