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Master Using Exponents to Describe Numbers | Easy Guide

Demonstrate understanding of powers with integral bases and whole number exponents

Using exponents to describe numbers

Expanded powers

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Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with exponents

Using exponents to solve problems

Demonstrate understanding of rational numbers by comparing and ordering 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

Explain and apply the order of operations including exponents with and without technology

Order of operations (PEMDAS)

Identify the Order of Operations

Order of Operations — Word Problem

Determine the square root of positive rational numbers that are perfect squares

Determine square roots of rational numbers

Square roots of rational numbers

Squares and square roots

Square Root of a Perfect Square

Determine the approximate square root of positive rational numbers that are non-perfect squares

Estimating square roots

Generalize a pattern arising from a problem-solving context using linear equations

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

Graph linear relations analyze the graph and interpolate or extrapolate to solve problems

Understanding graphs of linear relationships

Linear relations

Understanding tables of values of linear relationships

Linear relation

Applications of linear relationships

Model and solve problems using linear equations of various forms

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

Solving linear equations with variables on both sides

Solving literal equations

Explain and illustrate strategies to solve single variable linear inequalities

Compound inequalities

Analyze the Alternate Form of Compound Inequalities: AND

Compound linear inequalities

Evaluate Compound Inequalities: And

Express linear inequalities graphically and algebraically

Graph the Inequality

Linear Inequalities – Word Problem 

Linear inequalities

Solving one-step linear inequalities

One-step Linear Inequalities

One-step linear inequalities

One-step Linear Inequalities Decimal

One-step Linear Inequalities Decimal with Fraction

One-step Linear Inequalities Fraction

Solve One Step Linear Inequalities Find Solution– Word Problem

One-step Linear Inequalities — Word Problem

Solving multi-step linear inequalities

Multi-step Linear Inequalities

Two-step Linear Inequalities

Multi-step linear inequalities

Two-step linear inequalities

Solve Multi-step Linear Inequalities – Word Problem 

Solve Multi Step Linear Inequalities Solve Equation – Word Problem

Solve Multi Step Linear Inequalities Equation – Word Problem

Demonstrate an understanding of polynomials

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

Model record and explain the operations of multiplication and division of polynomial expressions

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

Model and solve problems using linear equations

Model and solve one-step linear equations: ax = b, x/a = b

One-step Linear Equations

One Step Linear Equations — Word Problem

One-step equations

One-step Equations LHS

One-step Equations RHS

Model And Solve One Step Linear Equations Divide – Word Problem

Model And Solve One Step Linear Equations Multiply – Word Problem

Solving two-step linear equations using addition and subtraction: ax + b = c

Two-step Linear Equations

Solve Linear Equations Using Addition and Subtraction – Word Problem

Two-step Linear Equations — Word Problem

Solving two-step linear equations using multiplication and division: x/a + b = c

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

Solve Linear Equations Using Distributive Property – Word Problem

Describe the effect of various factors on the collection of data

Influencing factors in data collection

Data collection

Select and defend the choice of using either a population or a sample of a population

Sampling methods

Sampling Methods

Census and bias

Census and Bias

Classifying Bias

Develop and implement a project plan for the collection display and analysis of data

Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Bivariate, scatter plots and correlation

Demonstrate an understanding of the role of probability in society

Probability

Solve problems and justify the solution strategy using circle properties

Angles in a circle

Chord properties

Tangent properties

Determine the surface area of composite 3-D objects to solve problems

Surface area of 3-dimensional shapes

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

Demonstrate an understanding of similarity of polygons

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Demonstrate an understanding of line and rotation symmetry

Line symmetry

Rotational symmetry and transformations

Assignments

Challenge Zone

Foundation Review

Grade 9 Math

Develop number sense

Use patterns to describe the world and solve problems

Represent algebraic expressions in multiple ways

Collect display and analyze data to solve problems

Use direct or indirect measurement to solve problems

math

Intro

Ex. 1:

Ex. 2:

<p>- 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?<br />
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?<br />
Thanks for watching.</p>


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Overview

Using Exponents to Describe Numbers: A Comprehensive Guide

What You'll Learn

Identify the base and exponent components in exponential notation

Convert repeated multiplication into exponential form

Calculate the value of powers with positive and negative bases

Recognize how even and odd exponents affect the sign of negative bases

Apply exponential notation to solve volume problems with cubes

What You'll Practice

Writing repeated multiplication as powers with given bases

Converting exponential expressions back to repeated multiplication

Completing tables relating multiplication, exponential form, and values

Working with negative bases and determining sign based on exponents

Expressing cube volumes using exponential notation

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

10 Video lessons

Practice exercises

Learning resources

Skills

Exponents

Base and Exponent

Exponential Notation

Powers

Repeated Multiplication

Negative Bases

Volume