Do Now: 10/28Do Now: 10/2843

a

1. Translate this expression: 96 more than an unknown number

2. Solve the equation algebraically:

3. Solve the following literal equation for H: V = LWH

4.

43

a

LEQ: What are LEQ: What are exponents and how can exponents and how can I use them to multiply, I use them to multiply, divide, +/-?divide, +/-?

Vocabulary Rating Vocabulary Rating ScaleScale 5 minutes to complete a self-5 minutes to complete a self-

assessment vocabulary for assessment vocabulary for Exponent UnitExponent Unit

glossary

Lesson LaunchLesson Launch1. Draw a representation of 31. Draw a representation of 33 3 (MP4)(MP4)

2. Explain how this is different from 3 X 3 2. Explain how this is different from 3 X 3 (MP2)(MP2)

  Share and discuss your responses. Share and discuss your responses.

ExponentsExponentsWhen a number is written with an When a number is written with an exponent, we say its in exponent, we say its in exponential exponential formform..

The The basebase is the is the factorfactor being being multiplied, and the multiplied, and the exponentexponent shows shows the number of times the base is the number of times the base is used as a factor.used as a factor.

4422 = 4 = 4 ▪ 4 = 16▪ 4 = 16base

exponent

factors

ExponentsExponents Define it in your own wordsDefine it in your own words

What’s the Rule for Multiplying What’s the Rule for Multiplying Exponents?Exponents?

Was Your Rule Correct?Was Your Rule Correct?What is 5 What is 5 44 ▪ 5 ▪ 5 22 in exponential form? in exponential form?(exponential form means the answer is written with exponents)(exponential form means the answer is written with exponents)

5544 = 5 = 5 ▪ 5 ▪ 5 ▪ 5▪ 5 ▪ 5 ▪ 55522 = 5 ▪ 5 = 5 ▪ 5

So, 5So, 544 ▪ 5 ▪ 522 = (5 ▪ 5 ▪ 5 ▪ 5) ▪ (5 ▪ 5) = 5 = (5 ▪ 5 ▪ 5 ▪ 5) ▪ (5 ▪ 5) = 566

5 is used as a factor 6 times.5 is used as a factor 6 times.

Notice that the exponent in the product Notice that the exponent in the product is the sum of the exponents in the is the sum of the exponents in the factors.factors.

SHORTCUT!: To multiply two numbers in exponential form SHORTCUT!: To multiply two numbers in exponential form with bases that are the samewith bases that are the same

StepsSteps1)keep the base 1)keep the base 2) add the exponents.2) add the exponents.

Formula: Formula: x x aa ▪ x ▪ x bb = x = x a + ba + b

5544 ▪ 5 ▪ 522 = 5 = 54 + 24 + 2 = 5 = 566

7733 ▪ 7 = 7 ▪ 7 = 73 + 13 + 1 = 7 = 744

22aa 55 ▪ 4▪ 4aa 22 = = (2 ▪ 4)(2 ▪ 4)aa 55 + 2+ 2 = 8 = 8aa 77

If the bases are

different, just

MULTIPLY the bases.

You will STILL ADD the

exponents

Our PracticeOur Practice

Exponents MultiplyingExponents Multiplying

Independent Practice

11

21

31

41

61

51

71

Example 2Example 2What is 3 What is 3 7 7 ÷ 3 ÷ 3 55 in exponential form? in exponential form?

3377 = 3 = 3 ▪ 3 ▪ 3 ▪ 3 ▪ 3 ▪ 3 ▪ 3▪ 3 ▪ 3 ▪ 3 ▪ 3 ▪ 3 ▪ 33355 = 3 ▪ 3 ▪ 3 ▪ 3 ▪ 3 = 3 ▪ 3 ▪ 3 ▪ 3 ▪ 3

Rewrite in fraction form and cross out common Rewrite in fraction form and cross out common factors.factors.3 ▪ 3 ▪ 3 ▪ 3 ▪ 3 ▪ 3 ▪ 33 ▪ 3 ▪ 3 ▪ 3 ▪ 3 ▪ 3 ▪ 3 3 ▪ 3 3 ▪ 3 3322

3 ▪ 3 ▪ 3 ▪ 3 ▪ 33 ▪ 3 ▪ 3 ▪ 3 ▪ 3 1 1

Notice that the Notice that the quotient exponent quotient exponent is the is the differencedifference between the between the dividend exponentsdividend exponents and and divisor exponentsdivisor exponents..

SHORTCUT!: To divide two numbers SHORTCUT!: To divide two numbers in exponential form with bases that in exponential form with bases that are the same, keep the base and are the same, keep the base and subtract the exponents.subtract the exponents.

x x aa = = x x a – ba – b

Formula:Formula: x x bb

Ex. 1:Ex. 1: 6688 = 6 = 68 – 58 – 5 = 6 = 633

6655

Ex. 2:Ex. 2: 3 3aa 55 = 3 = 3 aa 5 – 25 – 2 = 3 = 3aa 33

2a 2a 22 2 2 2 2

Power of a PowerPower of a Power

To simplify a number that has a To simplify a number that has a power raised to another power, power raised to another power, multiply the exponents and keep multiply the exponents and keep the base.the base.

FormulaFormula ((x x aa))bb = = xx abab

Example 3Example 3

Simplify: (5 Simplify: (5 33) ) 2 2

(5(533))22 = 5 = 53 3 ▪ 2▪ 2 = 5 = 566

Simplify:Simplify: (3a (3a 22) ) 33

(3(3aa 22))33 = (3) = (3)33 ▪ ( ▪ (aa 22))33 = 27 = 27aa 66

Negative ExponentsNegative ExponentsA base with a negative exponent A base with a negative exponent equals the reciprocal of the base equals the reciprocal of the base with a positive exponent.with a positive exponent.

In other words, write the expression as the In other words, write the expression as the denominator of a fraction with 1 as the denominator of a fraction with 1 as the numerator.numerator.

FormulaFormula x x – a– a = 1 = 1 x x aa

Example 4Example 4Write each of the following as a Write each of the following as a fraction:fraction:

5 5 -3-3 = 1 = 1 = 1 = 1 5533 125 125

8 8 -2-2 = 1 = 1 = 1 = 1 8822 64 64

More ExamplesMore Examples A negative base with an even exponent A negative base with an even exponent

equals a positive number.equals a positive number.(-3)(-3)22 = (-3) = (-3) ▪ (-3) = 9▪ (-3) = 9

A negative base with an odd exponent A negative base with an odd exponent equals a negative number.equals a negative number.

(-3)(-3)33 = (-3) ▪ (-3) ▪ (-3) = -27 = (-3) ▪ (-3) ▪ (-3) = -27

A base with a negative sign in front equals A base with a negative sign in front equals a negative number.a negative number.

-3-333 = -(3 ▪ 3 ▪ 3) = -27 = -(3 ▪ 3 ▪ 3) = -27

A base with an exponent of 0 equals 1.A base with an exponent of 0 equals 1.101000 = 1 = 1 23423400 = 1 = 1

HOMEWORKHOMEWORKComplete WorksheetComplete Worksheet

““ExponentsExponents””