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Master Using Exponents to Describe Numbers | Easy Guide

PAT: Master Provincial Achievement Test Skills

Operations with Decimals

test

Adding and subtracting decimals

Subtracting Decimals — Data Table

Ordering Decimals — Data Table

Decimals – Word Problem

Adding Decimals

Subtracting Decimals

Multiplying decimals

Multiplying Decimals

Dividing decimals 

Dividing Decimals

Order of operations (BEDMAS)

Mixed Operations with Decimals

Mixed Operations

Identify the Order of Operations

Order of Operations — Word Problem

Mixed Operations with Decimals Bracket

Mixed Operations with Bracket Square

Square Roots

Squares and square roots

Square Root of a Perfect Square

Estimating square roots

Rational Numbers

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Comparing and ordering rational numbers

Comparing decimal numbers

Comparing fractions

Solving problems with rational numbers in decimal form

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

Introduction to Linear Relations

Understanding graphs of linear relationships

Linear relations

Understanding tables of values of linear relationships

Linear relation

Applications of linear relationships

Linear Relations

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

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

Introduction to Polynomials

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

What is a polynomial?

Classifying Polynomials

Polynomial components

Operations with Polynomials

Adding and subtracting 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

Circle Geometry

Angles in a circle

Chord properties 

Tangent properties

Surface Area of 3D Objects

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

Scale Factors and Similarity

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Symmtery

Line symmetry

Rotational symmetry and transformations

Influencing factors in data collection

Data collection

Probability

Provincial Achievement Test

sample

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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