Chapter 6 Lesson 6-1

Essential Question What does anything to the zero power equal? How do I evaluate a number with a negative exponent? In the term 𝑥 3 , which term is the base and which is the exponent?

Base x Exponent Remember! 4

Positive Exponents We have seen positive exponents. Example 1: 5 4 =5∗5∗5∗5 Multiply the number by itself 4 times. Example 2: 𝑥 7 =𝑥∗𝑥∗𝑥∗𝑥∗𝑥∗𝑥∗𝑥 It works the same for numbers and variables.

Your Turn Example 3: 12 3 = ? 12∗12∗12 Example 4: 𝑧 5 = ? z∗𝑧∗𝑧∗𝑧∗𝑧

Your Turn Let us go the other direction Example 4: 𝑚∗𝑚∗𝑚= ? 𝑚 3 𝑞∗𝑞= ? 𝑞 2

Zero Exponent ANYTHING to the zero exponent is 1. Example 6: 9 0 = ? 1 3.14159265359 0 = ? Example 8: Numbers and variables work the same way. 𝑝 0 = ?

Negative Numbers with Positive and Zero Exponents When we have negative numbers with exponents there are two ways we will see them. One way: −2 4 The other way: (−2) 4 The first way keeps the negative out front. −2 4 =− 2∗2∗2∗2 =−16 The second way may change the sign. (−2) 4 = −2 ∗ −2 ∗ −2 ∗ −2 =16 Variables work the same way. −𝑡 4 is not the same as (−𝑡) 4 These are different. They give two different answers!!

Negative Numbers with Positive and Zero Exponents Continued… When we have negative numbers with exponents there are two ways we will see them. One way: −9 0 The other way: (−9) 0 The first way keeps the negative out front. −9 0 =−1 The second way may change the sign. (−9) 0 =1 Variables work the same way. −ℎ 0 =−1 and (−ℎ) 0 =1 These are different. They give two different answers!!

Negative Exponents If the number is on TOP, move it to the bottom. If the number is on BOTTOM, move it to the top.

Example 9: Move the number to the bottom and make the exponent POSITIVE 2 −3 1 2 3 = 1 2∗2∗2 = 1 8

Example 10: Move the variable to the bottom and make the exponent POSITIVE 𝑑 −4 1 𝑑 4

Example 11: 𝑎 0 𝑑 −4 𝑎 0 𝑑 4 = 1 𝑑 4 Move the variable to the bottom and make the exponent POSITIVE ANYTHING TO THE ZERO POWER IS 1.

Example 12: 5 𝑓 −7 5 𝑓 7 1 5𝑓 7 Move the variable to the top and make the exponent POSITIVE

Your Turn Example 13: 8 −2 1 64 Example 14: 5 0 𝑚 −2 𝑛 6 1 𝑚 2 𝑛 6

Your Turn Example 15: 3𝑦 −2 3 𝑦 2 Example 16: 𝑥 −3 𝑧 0 𝑦 −5 𝑦 5 𝑥 3

More Examples On the Board See white board. Homework page 395 (24-64 even)