Do Now: 10/28 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.

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

Vocabulary Rating Scale 5 minutes to complete a self- assessment vocabulary for Exponent Unit 5 minutes to complete a self- assessment vocabulary for Exponent Unit glossary glossary glossary

Lesson Launch 1. Draw a representation of 3 3 (MP4) 2. Explain how this is different from 3 X 3 (MP2) Share and discuss your responses.

Exponents When a number is written with an exponent, we say its in exponential form. The base is the factor being multiplied, and the exponent shows the number of times the base is used as a factor. 4 2 = 4 ▪ 4 = 16 base exponent factors

Exponents Define it in your own words Define it in your own words

What’s the Rule for Multiplying Exponents?

Was Your Rule Correct? What is 5 4 ▪ 5 2 in exponential form? (exponential form means the answer is written with exponents) 5 4 = 5 ▪ 5 ▪ 5 ▪ = 5 ▪ 5 So, 5 4 ▪ 5 2 = (5 ▪ 5 ▪ 5 ▪ 5) ▪ (5 ▪ 5) = is used as a factor 6 times. Notice that the exponent in the product is the sum of the exponents in the factors.

SHORTCUT!: To multiply two numbers in exponential form with bases that are the same Steps 1)keep the base 2) add the exponents. Formula: x a ▪ x b = x a + b 5 4 ▪ 5 2 = = ▪ 7 = = 7 4 2a 5 ▪ 4a 2 = (2 ▪ 4)a = 8a 7 If the bases are different, just MULTIPLY the bases. You will STILL ADD the exponents

Our Practice

Exponents Multiplying Independent Practice

Example 2 What is 3 7 ÷ 3 5 in exponential form? 3 7 = 3 ▪ 3 ▪ 3 ▪ 3 ▪ 3 ▪ 3 ▪ = 3 ▪ 3 ▪ 3 ▪ 3 ▪ 3 Rewrite in fraction form and cross out common factors. 3 ▪ 3 ▪ 3 ▪ 3 ▪ 3 ▪ 3 ▪ 3 3 ▪ ▪ 3 ▪ 3 ▪ 3 ▪ ▪ 3 ▪ 3 ▪ 3 ▪ 3 1 Notice that the quotient exponent is the difference between the dividend exponents and divisor exponents.

SHORTCUT!: To divide two numbers in exponential form with bases that are the same, keep the base and subtract the exponents. x a = x a – b Formula:x b Ex. 1:6 8 = 6 8 – 5 = Ex. 2: 3a 5 = 3 a 5 – 2 = 3a 3 2a a 2 2 2

Power of a Power To simplify a number that has a power raised to another power, multiply the exponents and keep the base. Formula (x a ) b = x ab

Example 3 Simplify: (5 3 ) 2 (5 3 ) 2 = 5 3 ▪ 2 = 5 6 Simplify: (3a 2 ) 3 (3a 2 ) 3 = (3) 3 ▪ (a 2 ) 3 = 27a 6

Negative Exponents A base with a negative exponent equals the reciprocal of the base with a positive exponent. In other words, write the expression as the denominator of a fraction with 1 as the numerator. In other words, write the expression as the denominator of a fraction with 1 as the numerator. Formulax – a = 1 x a x a

Example 4 Write each of the following as a fraction: 5 -3 = 1 = = 1 =

More Examples A negative base with an even exponent equals a positive number. A negative base with an even exponent equals a positive number. (-3) 2 = (-3) ▪ (-3) = 9 A negative base with an odd exponent equals a negative number. A negative base with an odd exponent equals a negative number. (-3) 3 = (-3) ▪ (-3) ▪ (-3) = -27 A base with a negative sign in front equals a negative number. A base with a negative sign in front equals a negative number = -(3 ▪ 3 ▪ 3) = -27 A base with an exponent of 0 equals 1. A base with an exponent of 0 equals = = 1

HOMEWORK Complete Worksheet “ Exponents ”