Today:Exponents, Exponents, Exponents;

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February 18, 2014

Vocabulary & Formulas Section of Notebook

Exponents are the mathematician's shorthand.

In general, the format for using exponents is:

(base)exponent

where the exponent tells you how many of the base are being multiplied together.

A Summary of Exponent Rules

1. 2.

5.

6. 7.

8.

3. Also Known as the power of a power rule.

4.

Common Errors with Exponents

Understanding Exponent Rules

Solve:

Practice Problem Section of Notebook

Understanding Exponent Laws:

Understanding Exponent Laws:

Understanding Exponent Laws:

Understanding Exponent Laws:

Practice Problems

1. 72

2. (-8)2

3. (-9) 3

4. -24

5. -43

Understanding Exponent Laws:

Exponent Laws

Simplify to lowest terms:

Exponent Laws

1. p2 • p4 • q3 • q5 =

p6q8

Only exponents of the same bases can be added.

Power of a Power Property

To find the power of a power, multiply the exponents.

Exponents: Zero and One as Exponents

When you have a 0 as an exponent, your answer will always almost always be 1. The only exception One exception is 00, which is undefined. But there are others:

40 = 1 50000 = 1 50 = 1 (-5)0 = 1 -(5)0 = -1

- (-5)0 = -1

“When you have a 0 as an exponent, your answer will always be 1.The only exception is 00, which is undefined”.

This is what the algebra text said about 0 as an exponent:

But this is incorrect. What they meant to say is:

Negative and Zero Exponents

Take a look at the following problems and see if you can find the pattern.

The expression a-n is the reciprocal of an

Examples:

Example 1

Example 2

Since 2/3 is in parenthesis, we must apply the power of a quotient property and raise both the 2 and 3 to the negative 2 power. First take the reciprocal to get rid of the negative exponent. Then raise (3/2) to the second power.

Negative and Zero Exponents

Example 3

Step 1:

Step 2:

Step 3:

Negative and Zero Exponents

Example 4:

Step 1:

Negative and Zero Exponents

Step 2:

Step 3:

Step 4:

Negative and Zero Exponents

Step 5:

Step 6-7:

Negative and Zero Exponents

Practice Problems

Negative Exponents: Answers

Negative Exponents: Answers

Negative Exponents: Answers