Lesson 8.3 Define and Use Zero and Negative Exponents After today’s lesson, you should be able to use zero and negative to simplify expressions. (CA 2.0)

PowerValue

Zero Exponent

Definition: Zero exponent

Examples: Simplify.

PowerValue

Negative Exponents Using Patterns to Discover the Meaning Behind Negative Exponents

Complete the following table. Use only a base of 10. Stand. FormExpanded FormExpon. Form 100,000 10,

Complete the following table. Use only a base of 10. Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙10 10,

Complete the following table. Use only a base of 10. Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙ ,

Complete the following table. Use only a base of 10. Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙ ,00010∙10∙10∙

Complete the following table. Use only a base of 10. Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙ ,00010∙10∙10∙

Complete the following table. Use only a base of 10. Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙ ,00010∙10∙10∙ ∙10∙

Complete the following table. Use only a base of 10. Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙ ,00010∙10∙10∙ ∙10∙

Complete the following table. Use only a base of 10. Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙ ,00010∙10∙10∙ ∙10∙ ∙

Complete the following table. Use only a base of 10. Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙ ,00010∙10∙10∙ ∙10∙ ∙

Complete the following table. Use only a base of 10. Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙ ,00010∙10∙10∙ ∙10∙ ∙

Complete the following table. Use only a base of 10. Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙ ,00010∙10∙10∙ ∙10∙ ∙

Complete the following table. Use only a base of 10. Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙ ,00010∙10∙10∙ ∙10∙ ∙

Now let’s continue the pattern. Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙ ,00010∙10∙10∙ ∙10∙ ∙ ,000

Now let’s continue the pattern. Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙ ,00010∙10∙10∙ ∙10∙ ∙ ,000

Now let’s continue the pattern. Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙ ,00010∙10∙10∙ ∙10∙ ∙ ,000

Now let’s continue the pattern. Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙ ,00010∙10∙10∙ ∙10∙ ∙ ∙ ,000

Now let’s continue the pattern. Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙ ,00010∙10∙10∙ ∙10∙ ∙ ∙ ,000

Now let’s continue the pattern. Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙ ,00010∙10∙10∙ ∙10∙ ∙ ∙ ∙10∙ ,000

Now let’s continue the pattern. Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙ ,00010∙10∙10∙ ∙10∙ ∙ ∙ ∙10∙ ,000

Now let’s continue the pattern. Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙ ,00010∙10∙10∙ ∙10∙ ∙ ∙ ∙10∙ , ∙10∙10∙10

Now let’s continue the pattern. Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙ ,00010∙10∙10∙ ∙10∙ ∙ ∙ ∙10∙ , ∙10∙10∙

What should you learn from this? Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙ ,00010∙10∙10∙ ∙10∙ ∙ ∙ ∙10∙ , ∙10∙10∙

What should you learn from this? Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙ ,00010∙10∙10∙ ∙10∙ ∙ ∙ ∙10∙ , ∙10∙10∙ ) Any number raised to the zero power is always 1.

What should you learn from this? Stand. FormExpanded FormExpon. Form 100,00010∙10∙10∙10∙ ,00010∙10∙10∙ ∙10∙ ∙ ∙ ∙10∙ , ∙10∙10∙ ) Any number raised to the zero power is always 1. 2) A negative exponent will create a fraction.

A negative exponent will result in the reciprocal of the base with a positive exponent.

5 -2 =

A negative exponent will result in the reciprocal of the base with a positive exponent = 1515 ( ) 2

A negative exponent will result in the reciprocal of the base with a positive exponent = 1515 ( ) 2 = 1515 ∙ 1515 = 1 25

A negative exponent will result in the reciprocal of the base with a positive exponent =

A negative exponent will result in the reciprocal of the base with a positive exponent = 1414 ( ) 3

A negative exponent will result in the reciprocal of the base with a positive exponent = 1414 ( ) 3 = 1414 ∙ 1414 = 1 64 ∙ 1414

A negative exponent will result in the reciprocal of the base with a positive exponent =

A negative exponent will result in the reciprocal of the base with a positive exponent = 1313 ( ) 4

A negative exponent will result in the reciprocal of the base with a positive exponent = 1313 ( ) 4 = 1313 ∙ 1313 = 1 81 ∙ 1313 ∙ 1313

A negative exponent will result in the reciprocal of the base with a positive exponent. (-6) -3 =

( ) A negative exponent will result in the reciprocal of the base with a positive exponent. = (-6) -3

( ) A negative exponent will result in the reciprocal of the base with a positive exponent. = = ∙ = ∙ (-6) -3

Practice Time

Evaluate. 1)2 -3 =2)4 -4 = 3)(-2) -4 =4)(-5) -3 = 5)8 0 = 6)(-4) 0 =

Evaluate. 1)2 -3 =2)4 -4 = 3)(-2) -4 =4)(-5) -3 = 5)8 0 = 6)(-4) 0 = 1818

Evaluate. 1)2 -3 =2)4 -4 = 3)(-2) -4 =4)(-5) -3 = 5)8 0 = 6)(-4) 0 =

Evaluate. 1)2 -3 =2)4 -4 = 3)(-2) -4 =4)(-5) -3 = 5)8 0 = 6)(-4) 0 =

Evaluate. 1)2 -3 =2)4 -4 = 3)(-2) -4 =4)(-5) -3 = 5)8 0 = 6)(-4) 0 =

Evaluate. 1)2 -3 =2)4 -4 = 3)(-2) -4 =4)(-5) -3 = 5)8 0 = 6)(-4) 0 =

Evaluate. 1)2 -3 =2)4 -4 = 3)(-2) -4 =4)(-5) -3 = 5)8 0 = 6)(-4) 0 =

Evaluate. Remember the order of operations. 1) = 2) 5 0 – (6) -2 = 3)4(3 + 5) = 4) (3 + 5) -2 =

Evaluate. Remember the order of operations. 1) = 2) 5 0 – (6) -2 = 3)4(3 + 5) = 4) (3 + 5) -2 = 3 16

Evaluate. Remember the order of operations. 1) = 2) 5 0 – (6) -2 = 3)4(3 + 5) = 4) (3 + 5) -2 =

Evaluate. Remember the order of operations. 1) = 2) 5 0 – (6) -2 = 3)4(3 + 5) = 20 4) (3 + 5) -2 =

Evaluate. Remember the order of operations. 1) = 2) 5 0 – (6) -2 = 3)4(3 + 5) = 20 4) (3 + 5) -2 =

Evaluate. Remember the order of operations. 5) (-2) -2 = 6) 5 2 – 3 0 = 7)2(1 + 3) -2 = 8) (6 + 3) 2 + (6 + 3) -2 =

Evaluate. Remember the order of operations. 5) (-2) -2 = 6) 5 2 – 3 0 = 7)2(1 + 3) -2 = 8) (6 + 3) 2 + (6 + 3) -2 = 3434

Evaluate. Remember the order of operations. 5) (-2) -2 = 6) 5 2 – 3 0 = 7)2(1 + 3) -2 = 8) (6 + 3) 2 + (6 + 3) -2 =

Evaluate. Remember the order of operations. 5) (-2) -2 = 6) 5 2 – 3 0 = 7)2(1 + 3) -2 = 8) (6 + 3) 2 + (6 + 3) -2 =

Evaluate. Remember the order of operations. 5) (-2) -2 = 6) 5 2 – 3 0 = 7)2(1 + 3) -2 = 8) (6 + 3) 2 + (6 + 3) -2 =

Definition: Negative exponent

Examples: Evaluate the expression.

Examples: Simplify the expression. Write your answer using only positive exponents.