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Master Exponent Rules: Simplify Math with Powers

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

Parent Assignments

Challenge Zone

Foundation Review

8th Grade Math

sample

math

Intro

Ex. 1:

Ex. 2:

Ex. 3:

Ex. 5:

Ex. 4:

Simplifying a power raised to a power using the power rule

Rewriting (7/8)^6 as a quotient of powers and calculating

Simplifying powers of 2 using power rule and product rule

Simplifying (-6)^4 · (-6)^2 ÷ (-6)^3 using exponent rules

Evaluating (-5^0)^3 using zero and odd exponent rules

Understanding the difference between powers, bases, and exponents

<p>- Hi. Welcome to this question right here. So what we have here is that write each expression as a single power. Then, calculate, okay? What we have here is this, if you look at it very carefully, it's 4 to the power of 3 times 4 to the power of 4. So the base number must be the same and when you're multiplying all you have to do is just add the exponents together. So what we have is that, if the base numbers the same, this number right here and this number here can now be added together, okay? But it's given that that base for both numbers are identical, okay?<br />
So what happened is you just have to recopy the base over and then it's simply 3 plus 4 on the top. I'm just showing a little bit of my work. It's just 4 to the power of 7, okay? It becomes your single power form which is right there and that's my little arrow sign, okay? Which is 4 to the power of 7. And we use a calculator to help us because the number gets too big again. It's just equal to 1-6-3-8-4 and that is your final answer. Thanks for watching.</p>


Multiplying powers with the same base using the product rule

Multiplying 3^2 times 3^5 using the product rule

Multiplying (-7)^3 times (-7)^3 using the product rule

Dividing powers with the same base using exponent subtraction

Simplifying 6^4 divided by 6^1 using the quotient rule

Rewriting (2 × -7)^3 as a product of two powers

Dividing negative 5 to the 6th by negative 5 to the 4th

Numbers with power can look complicated and difficult to calculate. Luckily, we can use exponent rules to simplify those expressions for a clear look and easier calculation.

Learning the laws and rules of exponents

Determining common multiples

Multiplying integers

Exponent Rules: The Key to Mastering Powers in Math

What You'll Learn

Multiply powers with the same base by adding exponents together

Divide powers with the same base by subtracting exponents

Apply the power rule to simplify expressions with exponents raised to exponents

Recognize the difference between base, exponent, and power in mathematical notation

Determine when a result is positive or negative based on the exponent value

What You'll Practice

Multiplying exponential expressions with identical bases

Dividing powers and simplifying using exponent subtraction

Applying power to a power rule by multiplying exponents

Calculating final numerical values from simplified exponential forms

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

13 Video lessons

Practice exercises

Learning resources

Skills

Exponents

Power Rules

Product of Powers

Quotient of Powers

Power to a Power

Simplification

Base and Exponent