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Master Using Exponents to Describe Numbers | Easy Guide

8.EE.A.1

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

Product rule of exponents

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Simplify the power

8.EE.A.2

Squares and square roots

Square Root of a Perfect Square

Square and square roots

Cubic and cube roots

Cube root of a perfect cube

Converting radicals to mixed radicals

Converting radicals to entire radicals

8.EE.A.3

Scientific notation

8.EE.B.5

Parallel and perpendicular lines in linear functions

Understanding graphs of linear relationships

Linear relations

Understanding tables of values of linear relationships

Linear relation

Applications of linear relationships

Identifying proportional relationships

8.EE.B.6

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

Slope intercept form: y = mx + b

8.EE.C.7

Introduction to 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

Two-step Linear Equations LHS

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

Two-step Linear Equations RHS

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

Solve Linear Equations Using Distributive Property – Word Problem

Solving literal equations

8.EE.C.8

Determining number of solutions to linear equations

Solving systems of linear equations by graphing

Solving systems of linear equations by elimination

Solving systems of linear equations by substitution

8.F.A.1

Relationship between two variables

Identifying functions

8.F.A.2

Function notation

8.F.B.4

Applications of linear relations

8.F.B.5

Graphing linear functions using table of values

8.G.A.1

Line symmetry

Tessellations using translations and reflections

tessellations using translations and reflections

8.G.A.2

Rotational symmetry and transformations

8.G.A.3

Enlargements and reductions with scale factors

Tessellations using rotations

8.G.A.4

Similar polygons

8.G.A.5

Similar triangles

8.G.B.6

Pythagorean theorem

Pythagorean Theorem

8.G.B.7

Using the pythagorean relationship

8.G.B.8

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

Applications of pythagorean theorem

8.G.C.9

Volume of cylinders

Word problems relating volume of prisms and cylinders

Surface area and volume of cones

Surface area and volume of spheres

8.NS.A.1

Understanding the number systems

Rational vs. Irrational numbers

8.NS.A.2

Determine square roots of rational numbers

Square roots of rational numbers

Estimating square roots

Converting repeating decimals to fractions

8.SP.A.1

Reading linear relation graphs

Box-and-whisker plots and scatter plots

8.SP.A.2

Solving linear equations by graphing

8th Grade Math

sample

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>


Converting between repeated multiplication, exponential form, and values

Ex. 3:

Exponents with negative bases: even vs odd exponent rule

Ex. 4:

Finding the volume of a cube using exponents

Ex. 5:

Understanding the difference between powers, bases, and exponents

Writing 5 times 5 in exponential notation

Writing 4 × 4 × 4 in exponential notation

Writing 6×6×6×6×6 in exponential notation

Writing 8 multiplied seven times in exponential notation

Writing 16 as a negative base raised to the power of 4

Expressing 16 as a power with exponent four

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