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Master Using Exponents to Describe Numbers | Easy Guide

EQAO Grade 9 Math: Master Core Concepts & Skills

Ratios, Rates, and Proportions

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Ratios

Ratios - Find The Missing Value LHS

Ratios - Find The Missing Value RHS

Equivalent Ratios

Rates

Find the Biggest Rate 

Find the Unit Price 

Unit Rate Fill in Box

Find the Quickest Rate 

Unit Rate

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

Square Roots

Squares and square roots

Square Root of a Perfect Square

Estimating square roots

Pythagorean Theorem

Introduction to pythagorean theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Rational Numbers

Comparing and ordering rational numbers

Comparing decimal numbers

Comparing fractions

Solving problems with rational numbers in decimal form

Mixed Operations with Decimals

Mixed Operations

Mixed Operations with Decimals Bracket

Mixed Operations with Bracket Square

Solving problems with rational numbers in fraction form

Operations with fractions

Determine square roots of rational numbers

Square roots of rational numbers

Powers and Exponents

Using exponents to describe numbers

Expanded powers

Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with exponents

Using exponents to solve problems

Proportional Relationships

Understanding graphs of proportional relationships

Linear relations

Using tables of values to graph proportional relationships

Linear relation

Applications of proportional relationships

Identifying proportional relationships

Linear Ralations

Representing patterns in linear relations

Represent Patterns in Linear Relations Equation Decimal

Represent Patterns in Linear Relations Equation Integer Start From 0

Represent Patterns in Linear Relations Equation Integer Start From 1

Represent Patterns in Linear Relations Equation Negative Decimal

Identify the Linear Equation

Reading linear relation graphs

Solving linear equations by graphing

Solving Linear Equations

Solving linear equations using multiplication and division

Two-step Linear Equations LHS

Two-step Linear Equations RHS

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations with variables on both sides

Introduction to Relations and Functions

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Linear Functions

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Slope intercept form: y = mx + b

General form: Ax + By + C = 0

Point-slope form: \(y - y_1 = m (x - x_1)\)

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

Introduction to Polynomials

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

Multiplication and Division of Polynomials

Multiplying and dividing monomials 

Divide a monomial by a monomial

Multiply a monomial by a monomial

Multiplying polynomials by monomials

Multiply a polynomial by a monomial

Dividing polynomials by monomials

Introduction to 3-Dimensional Objects

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface Area of Prisms Rectangle

Calculate the Surface Area

Surface area of cylinders

Surface Area and Volume

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Circle Geometry

Angles in a circle

Chord properties 

Tangent properties

Data Management

Influencing factors in data collection

Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Sampling methods

Sampling Methods

Scatter plots and correlation

Census and bias

Census and Bias

Classifying Bias

Linear Programming

What is linear programming?

Finding Optimal Values Given Constraints In Slope-Intercept Form

Finding Optimal Values Given Constraints In Standard Form

Linear programming word problems

EQAO Grade 9 Principles of Math

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Intro

Ex. 1:

Ex. 2:

- Hi. Welcome to this question right here. So sometimes we're given as a table just to demonstrate the relationship between the repeated multiplication and exponential form and the value of the answer. Okay? So what we have for the first part right here is that we&apos;ve got 9 times 9 times 9 times 9. Okay? But we can also change it into exponential form, which is 9, the base number, raised to the power of 4. That means it happens four times. Now, if you're going to calculate the value for that, it will be 9 to the power of 4. We&apos;ve got ourselves 6561 right there. Okay? 6561. So we're going to quickly fill out the rest of this table really quick. We&apos;ve got 2. The base number is 2. So we&apos;ve got 2 right there and raised to the power of three times. And 2 to the power of 3 is just 8. We have a 25 over here for the next question. So is there any number here multiplied by themselves maybe two or three times that gives 25? 
It's actually just 5 to the power of 2. Okay? You have to get used to all the powers. So what is 5 to the power of 2 anyway? Well, it means it's 5 times 5. Okay? The 5 raised to the power of 2 means that the 5 is multiplied by itself by two times. Okay? 216 right here. So what do we have for 216? That looks like a... That is such a weird number. Let me see what I have right here. Could it be 6 to the power of 3? I think so. So what we have is 6 to the power of 3. Now, how do we know that it's the base of 6 and it's raised to the power of 3 to give you 216? Sometimes you can actually do the prime factorization. But for now, it's best for you to go and memorize all the powers from 1 to 12, you know. At least you can recognize the first three, like for example, 6 to the power of 1 is 6, 6 to the power of 2 is 36, and hopefully you can see the 6 to the power of 3. Okay? But anyway, you're free of all of this later when you go to Math 10. Okay? So what will happen here is that 6 to the power of 3 means that 6 times itself three times. Okay? Next question, the final one: 12 to the power of 3, which is easier because we do know the base is 12 raised to the power of three times. It means 12 times itself three times. Okay? Again, use your calculator. Raise the power of 12 to power of 3. We&apos;ve got ourselves 1728. And that's the end of this question right here. Okay? 
Thanks for watching.

Ex. 3:

Ex. 4:

Ex. 5:

A number in exponential form has two components, the base and the exponent. The base is the bigger number on the left, and the exponent is the smaller number at the top right hand corner of the base. When you multiply the same number two times or more, you may express it in exponential form. 

How to use exponents to describe numbers

Determining common multiples

Understanding integer multiplication

Multiplying integers