Lesson 4.6 Negative and Zero Exponents Essential Question: How do you simplify powers with negative and zero exponents?

Before we start… Complete the table by determining the pattern. Power Value 2 3 8 2 2 4 2 1 2 2 0 2 −1 2 −2

Negative Exponents Negative Exponents Property Words For any integer n and any number 𝑎≠0, 𝑎 −𝑛 is equal to 1 𝑎 𝑛 Algebra 𝑎 −𝑛 = 1 𝑎 𝑛 Numbers 2 −3 = 1 2 3

Zero Exponents Zero Exponents Words For any number 𝑎≠0, 𝑎 0 =1 Algebra Numbers 2 0 =1

Write the expression using only positive exponents. 3 −5

Evaluate the expression 7 −2

Evaluate the expression 10 −5 ∙ 10 5

Simplify the expression −2 𝑛 0

Simplify the expression 8 𝑥 −3 𝑥

Simplify the expression − 5 𝑥 0 3

Simplify the expression 5 𝑥 4 𝑥 −7

Simplify the expression 𝑐 −1 ∙ 𝑐 −2 ∙ 𝑐 −4

Simplify the expression 𝑦 −6 ∙ 𝑦 9

Simplify the expression 𝑚 0 ∙ 𝑛 −4

Simplify the expression 16𝑥 −6 ∙𝑦

Simplify the expression 𝑎 −3 ∙ 𝑎 10

Simplify the expression 𝑏 −4 𝑏 −6

How do you simplify powers with negative and zero exponents?

Ticket Out the Door Simplify 𝑥 −6 ∙ 𝑥 2 𝑦 𝑥 5 𝑦 4