Indices – The Six Basic Index Laws 1 st Law 5 3 x 5 4 = (5 x 5 x 5) x (5 x 5 x 5 x 5)= 5 7 Example: aax=a + mnmn.

Slides:

Advertisements

Similar presentations

Laws of Indices or Powers © Christine Crisp. Laws of Indices Generalizing this, we get: Multiplying with Indices e.g.1 e.g.2.

Advertisements

1 st Place Post-Secondary Winner. 2 nd Place Post-Secondary Winner.

Chapter 11 Sequences and Series Arithmetic Sequences.

Index Laws Miss Hudson’s Maths.

Problem Solving Process

1.4 – The Distributive Property. a(b+c)=ab+ac and (b+c)a=ba+ca.

Geometric Sequences and Series Part III. Geometric Sequences and Series The sequence is an example of a Geometric sequence A sequence is geometric if.

Arithmetic Sequences and Series. A sequence is arithmetic if each term – the previous term = d where d is a constant e.g. For the sequence d = 2 nd term.

Arithmetic Sequences Explicit Formula.

Barton St Peter’s Advent Calendar.

Roots and Radicals. Radicals (also called roots) are directly related to exponents.

Radicals and Rational Indices. If x 2 = a, then x is a square root of a. Radicals Do you remember what square root means? For example: 3 2 = 9 3 is a.

To find the nth term of a sequence

Aim: What is the arithmetic sequence? Do Now: Find the first four terms in the sequence whose n th term is 4n + 3. HW: p.256 # 4,5,6,8,10,12,16,18,19,20.

U SING AND W RITING S EQUENCES The numbers (outputs) of a sequence are called terms. sequence You can think of a sequence as a set of numbers written in.

Aim: What is the geometric sequence?

U SING AND W RITING S EQUENCES The numbers (outputs) of a sequence are called terms. sequence You can think of a sequence as a set of numbers written in.

Indices and Exponential Graphs

 Life Expectancy is 180 th in the World.  Literacy Rate is 4 th in Africa.

Patterns and Sequences Sequence: Numbers in a specific order that form a pattern are called a sequence. An example is 2, 4, 6, 8, 10 and 12. Polygon:

CHAPTER 5 INDICES AND LOGARITHMS What is Indices?.

Arithmetic Recursive and Explicit formulas I can write explicit and recursive formulas given a sequence. Day 2.

Ch.9 Sequences and Series Section 1 - Mathematical Patterns.

1-2 Simplifying Expressions. Free powerpoints at

Index Laws Whenever we have variables which contain exponents and have equal bases, we can do certain mathematical operations to them. Those operations.

1-2 Simplifying Expressions.

Aim: What is the arithmetic sequence?

Arithmetic and Geometric Means

Aim: What is the arithmetic and geometric sequence?

Warm Up 1st Term:_____ 1st Term:_____ 2nd Term:_____ 2nd Term:_____

Warm Up 1st Term:_____ 1st Term:_____ 2nd Term:_____ 2nd Term:_____

The Derivative as a Function

9.4 Solving Quadratic Equations

Geometric Sequences and Series

Grade one First term Second term Learning unit Learning unit

Phone Number BINGO!!!.

Explanation of Grades to Numbers

Are You Smarter Than a 5th Grader?

Aim: What is the sequence?

4n + 2 1st term = 4 × = 6 2nd term = 4 × = 10 3rd term

Бази от данни и СУБД Основни понятия инж. Ангел Ст. Ангелов.

Kinder Campus Math Bee School Year.

Kinder Math Bee Counting Practice.

Square and Cube Roots Roots and Radicals.

Unit 3 Review (Calculator)

Kindergarten Math Bee Practice.

4 Years Milestone plan – (Company Name)

Kinder Math Bee Addition Practice.

Sequences and Summation Notation

Index Laws Objectives:

Surds Roots that are irrational are called surds. Law 1:

How to find the nth rule for a linear sequence

Kinder Campus Math Bee School Year.

Kinder Math Bee Practice Power point School Year.

Fractional Indices.

Before and After Practice

October 2014 Star Data Prior to the C.A.F.E. Reading Initiative these were the results attained.

WHS Bell Schedule 1st Period  7:30 – 8:30 2nd Period  8:35 – 9:30

Calculate 9 x 81 = x 3 3 x 3 x 3 x 3 3 x 3 x 3 x 3 x 3 x 3 x =

8.5 Using Recursive Rules with Sequences

Kindergarten Math Bee Practice.

Kinder Campus Math Bee Skill: Counting School Year.

Kinder Campus Math Bee School Year.

MONTHS OF THE YEAR Les docs d’Estelle Les docs d’Estelle

To calculate the number of combinations for n distinguishable items:

Sequences: Is a value a term in a sequence?

9 x 14 9 x 12 Calculate the value of the following: 1 7 × 5 =

Presentation transcript:

Indices – The Six Basic Index Laws 1 st Law 5 3 x 5 4 = (5 x 5 x 5) x (5 x 5 x 5 x 5)= 5 7 Example: aax=a + mnmn

Indices – The Six Basic Index Laws 2 nd Law 7 5 ÷ 7 2 == 7 3 Example: aa÷=a mn - mn 7 x 7 x 7 x 7 x 7 7 x 7

Indices – The Six Basic Index Laws 3 rd Law (3 2 ) 4 = (3 x 3) x (3 x 3) x (3 x 3) x (3 x 3) = 3 8 Example: a= a m n xm n

Indices – The Six Basic Index Laws 4 th Law Consider the sequence: Example: ½ ¼ a= a m 1 - m

Indices – The Six Basic Index Laws 5 th Law Consider the calculations: Example: 3 1/2 x 3 1/2 a=√a√a n = 3 1 = √3 x √3 1 n ‘the n th root of a’ = 3

Indices – The Six Basic Index Laws 6 th Law Example: 4 3/2 a= ( √a ) n = (√4) 3 = 8 m n m = (4 1/2 ) 3 ‘the n th root of a to the power of m’