7 2 A Zero and Negative Exponents Algebra

7 -2 A Zero and Negative Exponents Algebra 1 Glencoe Mc. Graw-Hill Linda Stamper

Inductive Reasoning is making conclusions based on patterns you observe. Today you will use patterns to formulate a rule for negative exponents and for nonzero numbers to the zero power. Before we look at some data, identify whether the following number is located in a numerator or a denominator position. What is the denominator?

Complete the chart. 2 -4 2 -3 2 -2 2 -1 20 21 22 23 24 The table shows 3 different ways to write the same value!

Complete the chart. 2 -4 2 -3 2 -2 2 -1 20 21 22 23 24 3 -3 3 -2 3 -1 30 31 32 33 34

Complete the chart. 2 -4 2 -3 2 -2 2 -1 20 21 22 23 24 3 -3 3 -2 3 -1 30 31 32 33 34 What rule can you formulate about a nonzero number to the zero power?

Complete the chart. 2 -4 2 -3 2 -2 2 -1 20 21 22 23 24 3 -3 3 -2 3 -1 30 31 32 33 34 What rule can you formulate about a nonzero number to the zero power? Any nonzero number to the zero power is 1.

I am going to remove the middle row. 2 -4 2 -3 2 -2 2 -1 20 21 22 23 24

What do you notice about the exponents? 2 -4 2 -3 2 -2 2 -1 20 21 22 23 24 When powers change position from the numerator to the denominator (or the denominator to the numerator), the sign of the exponent changes. 3 -4 3 -3 3 -2 3 -1 30 31 32 33 34

A simplified expression means positive exponents. A nonzero number to the zero power is 1. 20=1 Zero to the zero power is undefined! When moving a power (base and exponent) from numerator to denominator (or denominator to numerator), change the sign of the exponent. The exponent acts on the base and the base alone (not even on the sign of the base, unless the sign is in parentheses!). Copy all the above in your notebook!

Simplify the expression. Example 1 Example 2 Example 3 Example 4 Example 5 Example 6

Simplify the expression. Example 2 Example 1 Example 3 Simplified means no negative exponents! Example 4 Rewrite power with a positive exponent – move to denominator and change sign of exponent.

Simplify the expression. Example 5 Example 6

Simplify the expression. Example 7 Example 8 Example 9 Example 10 Example 11 Example 12

Simplify the expression. Example 7 Example 8 Rewrite power with positive exponent – move to denominator and change sign of exponent.

Simplify the expression. Example 9 Example 10

Simplify the expression. Example 11 Example 12

Practice Problems. Simplify the expression.

8 -A 3 Handout A 3.

Working with zero.