# Exponents Standard Exponent Tells how many times a

- Slides: 63

Exponents Standard:

Exponent: Tells how many times a base is used as a factor. Exponent 2³ = 2 ∙ 2 Base Power

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Common Exponents Squared: anything to the second power Example: 9² is 9 squared Cubed: anything to the third power Example: 10³ is 10 cubed

Zero Power: anything to the zero power is ONE! Example: 8⁰ = 1 (-24)⁰ = 1 2, 500, 050⁰ = 1

Problem of the DAY! What is the value of 7⁰? a. b. c. d. 1 0 7 1/7 Anything to the Power of Zero is ONE!

Remember! The exponent tells you how many times you will multiply the same number by itself! Even when it is negative! For example: (-5)³ = (-5) ∙ (-5) = 125

Negative numbers When the negative is inside the parenthesis, then it is the same negative number multiplied by itself When it is outside, you add the negative at the end!

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This time it’s different!

Example: Write using exponents: a∙b∙b∙b∙a a. b. c. d. 3 2 a b 2 3 a b 2 2 a b aabbb

And again! x ∙ y ∙ x ∙ x∙ x ∙ y ∙ x a. b. c. d. 6 2 xy x 5 y 2 6 x 2 y 2 5 xy

And again! Simplify (ab)³ using exponents. a. b. c. d. ababab a³b³ 3 a 3 b a²b²

Negative Exponents -n a = Example: 1 n a

Example 2

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Problem of the Day (Thursday) 4 What is (-12) ? a. b. c. d. 20736 -20736 48 -48

Exponents – Review!

Review 2

Review 3

Review 4 -2 What is 5 ? a. -25 b. 25 c. 1 25 d. 1 -25

Review 5 What is 3 x ∙ 3 x? a. b. c. d. 3 x³ 27 x 9 x 27 x³

Multiplying Exponents To multiply numbers or variables with the same base, add the exponents Example: 3³ ∙ 3² = 3∙ 3∙ 3= (3+2) 3 = 35 = 243

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Try again!

And again!

Dividing Exponents When dividing exponents, you subtract! 7 3 3² 3 (7 -2) 5 =3

Example 2

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And again! 99 Solve (-7) 98 (-7) a. -7 b. 1 c. 7 d. 7 97

And again! 4 Solve w w 6 a. w² b. -2 w c. w 2 d. 1 w²

Exponents Raised to a Power Example: (2⁵)² *Multiply the exponents

How to do it on your calculator!

Problem of the Day (Friday) 8 Write x ∙ x using a single exponent a. b. c. d. x 12 x 8 7 x 9 x

Problem of the Day (Tuesday) Write the number 124, 000 in scientific notation. a. b. c. d. 8 1. 24 x 10 6 1. 24 x 10 7 12. 4 x 10

Problem of the Day (Tuesday) Write the following using a positive exponent: 6 2 ∙ 6 -5 a. 6³ b. 1_ 6³ c. 1_ 5 6 d. 6 5

Review

Review

Scientific Notation

Why do we use it? Scientific notation is a way of writing extremely small or large numbers in a way that is easier.

Scientific Notation: A single digit (greater than or equal to 1 but less than 10) multiplied by a power of ten Example: 37, 000 in scientific notation 7 3. 7 x 10

The other way around 6 1. 55 x 10 in standard form 1, 550, 000

Write the number 124, 000 in scientific notation. a. b. c. d. 8 1. 24 x 10 6 1. 24 x 10 7 12. 4 x 10

Another example!

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Another example!

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If it is a number less than one: Use negative exponents! Example: 0. 000098 In scientific notation 9. 8 x 10 -5

Example 2

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And again!

Try with a partner

Try with a partner

Problem of the Day (Friday)

Order of Operations PEMDAS