# Exponents.

## Presentation on theme: "Exponents."— Presentation transcript:

Exponents

1. Relate and apply the concept of exponents (incl. zero). 2
1. Relate and apply the concept of exponents (incl. zero) Perform calculations following proper order of operations Applying laws of exponents to compute with integers Naming square roots of perfect squares through 225.

EXPONENT LAWS

Basic Terminology EXPONENT means BASE

IMPORTANT EXAMPLES

Variable Expressions

Substitution and Evaluating
STEPS Write out the original problem. Show the substitution with parentheses. Work out the problem. = 64

Evaluate the variable expression when x = 1, y = 2, and w = -3
Step 1 Step 1 Step 1 Step 2 Step 2 Step 2 Step 3 Step 3 Step 3

MULTIPLICATION PROPERTIES
PRODUCT OF POWERS This property is used to combine 2 or more exponential expressions with the SAME base.

MULTIPLICATION PROPERTIES
POWER TO A POWER This property is used to write and exponential expression as a single power of the base.

MULTIPLICATION PROPERTIES
POWER OF PRODUCT This property combines the first 2 multiplication properties to simplify exponential expressions.

MULTIPLICATION PROPERTIES
SUMMARY PRODUCT OF POWERS ADD THE EXPONENTS POWER TO A POWER MULTIPLY THE EXPONENTS POWER OF PRODUCT

ZERO AND NEGATIVE EXPONENTS
ANYTHING TO THE ZERO POWER IS 1.

DIVISION PROPERTIES QUOTIENT OF POWERS
This property is used when dividing two or more exponential expressions with the same base.

DIVISION PROPERTIES POWER OF A QUOTIENT Hard Example

ZERO, NEGATIVE, AND DIVISION PROPERTIES
Zero power Quotient of powers Negative Exponents Power of a quotient

0²= ²= ²=144 1²= ²= ²=169 2²= ²= ²=225 3²= ²= ²=256 4²= ²= ²=400 5²= ²= ²=625

Exponents in Order of Operations
1) Parenthesis →2) Exponents 3) Multiply & Divide 4) Add & Subtract

Exponents & Order of Operations

Contest Problems Are you ready? 3, 2, 1…lets go!

180 – 5 · 2²

Evaluate the expression when y= -3 (2y + 5)²

-3²

Warning. The missing parenthesis makes all the difference
Warning!!! The missing parenthesis makes all the difference. The square of a negative & the negative of a square are not the same thing! Example: (-2)² ≠ -2²

Contest Problems

Are you ready? 3, 2, 1…lets go!

8(6² - 3(11)) ÷ 8 + 3

Evaluate the expression when a= -2 a² + 2a - 6

Evaluate the expression when x= -4 and t=2 x²(x-t)

Exponent Rule: a ∙ aⁿ = a Example1: 2 ∙ 2 = 2¹⁺¹ = 2² = 4
m + n Example1: 2 ∙ 2 = 2¹⁺¹ = 2² = 4 Example2: 2³ ∙ 2² = 2³⁺² = 2⁵ = 32

Simplify (in terms of 2 to some power)
Simplify (in terms of 2 to some power). Your answer should contain only positive exponents. 4² · 4²

Simplify (in terms of 2 to some power)
Simplify (in terms of 2 to some power). Your answer should contain only positive exponents · 2² · 2²

Simplify. Your answer should contain only positive exponents. 2n⁴ · 5n ⁴

(-4)³

(-2)⁴

Important! *If a negative number is raised to an even number power, the answer is positive. *If a negative number is raised to an odd number power, the answer is negative.

Contest Problem Are you ready? 3, 2, 1…lets go!

(5²) (2⁵) (-1)

Exponent Rule: (ab)² = a²b² Example: (4·6)² = 4²·6²

Exponent Rule: (a/b)² = a²/b² Example: (7/12)² = 7²/12² = 49/144

Exponent Rule: (a÷b)ⁿ = aⁿ÷bⁿ = aⁿ/bⁿ
Example: (2÷5)³ = (2÷5)·(2÷5)·(2÷5) = (―)·(―)·(―) =(2·2·2)/(5·5·5) =2³/5³ = 8/125 2 5 2 5 2 5

Exponent Rule: (1/a)² = 1/a² Example: (1/7)² = 1/7² = 1/49

Exponent Rule: a ÷aⁿ = a m m - n Example: 2⁵ ÷ 2² = 2⁵¯² = 2³ = 8

m · n m Exponent Rule: (a )ⁿ = a 2·5 Example: (2²)⁵ = 2 = 2¹⁰ = 1,024

Exponent Rule: a⁰ = 1 Examples: (17)⁰ = 1 (99)⁰ = 1

Exponent Rule: (a)¯ⁿ = 1÷aⁿ
Example: 2¯⁵ = 1 ÷ 2⁵ = 1/32

Problems Are you ready? 3, 2, 1…lets go!

2 ( )

Simplify the following problems completely
Simplify the following problems completely. Your answer should not contain exponents. Example: 2³·2² = 2⁵ = 32

-3 - (1)¯⁵

(2)¯³

(-2)¯³

-2⁽¯⁴⁾

(2)¯³ · (-16)

56 · (2)¯³

56 ÷ (2)¯³

1 ÷ (-3)¯²

(2²)³ · (6 – 7)² - 2·3² ÷ 6

-6 - (-4)(-5) - (-6)

2 (10² + 3 · 18) ÷ (5² ÷ 2¯²)

Simplify: (x⁴y¯²)(x¯¹y⁵)

Competition Problems Points: 1 minute: 5 points 1 ½ minute: 3 points 2 minute: 1 point 3, 2, 1, … go!

Simplify: (4x4y)3 (2xy3)

If A = (7 – 11 + 8)131 and B = (–7 + 11 – 8)131 then what is the value of: (7 – 13)(A+B)

Simplify:

Evaluate for x = –2, y = 3 and z = –4:

If A♣B = (3A–B)3, then what is (2♣8)♣6?

If a*b is defined as (ab)2 + 2b, and x y is defined as xy2 - 2y, find 2*(3 4).

Simplify: 24 – 4(12 – 32 – 60)

If x = the GCF of 16, 20, and 72 and y = the LCM of 16, 20, and 72, what is xy?

Express in simplest form:

Simplify:

Simplify. Write the answer with negative exponents. (abc)-3c2b a-4bc2a

Simplify …

Solve for n:

. Solve for q: