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Master the 8 and 9 Laws of Indices: Easy Examples and Fun Worksheets

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abi

10/10/2022

Arithmetic

Index Laws

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Square Roots & Cube Roots

Master the 8 and 9 Laws of Indices: Easy Examples and Fun Worksheets

The laws of indices are fundamental rules for working with exponents in mathematics. These rules simplify calculations involving powers and are essential for algebra and higher mathematics.

  • Eight key laws of indices cover addition, subtraction, multiplication, and division of powers
  • These laws apply to various mathematical operations and are crucial for simplifying complex expressions
  • Understanding and applying these laws is vital for solving problems in algebra, calculus, and other advanced math topics
...

10/10/2022

389

VIR ya spås (₁) b ху b = = y y Index Laws a+b a-b (add powers) (subtract powers) = = yaxb (multiply powers) worked example m 4 x m 2 3r³ 8 =

View

Worked Examples: Applying Index Laws

This page demonstrates practical applications of the laws of indices through worked examples. These examples illustrate how to use the laws to simplify complex expressions.

The first example shows:

m^4 × m^2 = m^6

This utilizes the addition law of indices, where exponents with the same base are added.

Another example presented is:

3r^3 × 5r^4 × 2r^8 = 30r^15

Example: In this case, we multiply the coefficients 3×5×2=303 × 5 × 2 = 30 and add the exponents of r 3+4+8=153 + 4 + 8 = 15.

These worked examples help reinforce the understanding of how to apply index laws in various scenarios, which is crucial for mastering algebraic manipulation.

Highlight: Practicing with diverse examples is key to becoming proficient in using index laws.

VIR ya spås (₁) b ху b = = y y Index Laws a+b a-b (add powers) (subtract powers) = = yaxb (multiply powers) worked example m 4 x m 2 3r³ 8 =

View

Advanced Index Law Applications

This page delves into more complex applications of the laws of indices, showcasing how they can be used to solve more intricate problems.

One of the examples presented is:

12n^10 ÷ n^2 = n^8

This demonstrates the subtraction law of indices, where exponents are subtracted when dividing terms with the same base.

Another example shown is:

15n^12 ÷ 3n^6 = 5n^6

Example: Here, we divide both the coefficients 15÷3=515 ÷ 3 = 5 and subtract the exponents 12−6=612 - 6 = 6.

These examples illustrate how index laws can be applied to simplify fractions and complex algebraic expressions.

Highlight: The ability to manipulate expressions using index laws is a crucial skill in advanced algebra and calculus.

VIR ya spås (₁) b ху b = = y y Index Laws a+b a-b (add powers) (subtract powers) = = yaxb (multiply powers) worked example m 4 x m 2 3r³ 8 =

View

Complex Index Manipulations

The final page presents more advanced applications of the laws of indices, demonstrating their use in complex mathematical expressions.

One example shown is:

m24m^24^9 = m^216

This utilizes the multiplication law of indices, where the exponents are multiplied when a power is raised to another power.

Another example is:

3r23r^2^4 = 81r^8

Example: In this case, we raise both the base number and the variable to the power of 4: 3^4 = 81 and r2r^2^4 = r^8.

These examples showcase how index laws can be applied to solve complex problems involving nested exponents and multiple variables.

Highlight: Mastering these complex manipulations is essential for success in higher-level mathematics courses.

The page also includes additional examples that further reinforce the application of various index laws in different scenarios.

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Subjects

Arithmetic

Square & Cube Roots

Square Roots & Cube Roots

 

Arithmetic

•

389

•

Oct 10, 2022

•

4 pages

Master the 8 and 9 Laws of Indices: Easy Examples and Fun Worksheets

user profile picture

abi

@lvjyabi

The laws of indices are fundamental rules for working with exponents in mathematics. These rules simplify calculations involving powers and are essential for algebra and higher mathematics.

  • Eight key laws of indices cover addition, subtraction, multiplication, and division of powers... Show more

VIR ya spås (₁) b ху b = = y y Index Laws a+b a-b (add powers) (subtract powers) = = yaxb (multiply powers) worked example m 4 x m 2 3r³ 8 =

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Worked Examples: Applying Index Laws

This page demonstrates practical applications of the laws of indices through worked examples. These examples illustrate how to use the laws to simplify complex expressions.

The first example shows:

m^4 × m^2 = m^6

This utilizes the addition law of indices, where exponents with the same base are added.

Another example presented is:

3r^3 × 5r^4 × 2r^8 = 30r^15

Example: In this case, we multiply the coefficients 3×5×2=303 × 5 × 2 = 30 and add the exponents of r 3+4+8=153 + 4 + 8 = 15.

These worked examples help reinforce the understanding of how to apply index laws in various scenarios, which is crucial for mastering algebraic manipulation.

Highlight: Practicing with diverse examples is key to becoming proficient in using index laws.

VIR ya spås (₁) b ху b = = y y Index Laws a+b a-b (add powers) (subtract powers) = = yaxb (multiply powers) worked example m 4 x m 2 3r³ 8 =

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Advanced Index Law Applications

This page delves into more complex applications of the laws of indices, showcasing how they can be used to solve more intricate problems.

One of the examples presented is:

12n^10 ÷ n^2 = n^8

This demonstrates the subtraction law of indices, where exponents are subtracted when dividing terms with the same base.

Another example shown is:

15n^12 ÷ 3n^6 = 5n^6

Example: Here, we divide both the coefficients 15÷3=515 ÷ 3 = 5 and subtract the exponents 12−6=612 - 6 = 6.

These examples illustrate how index laws can be applied to simplify fractions and complex algebraic expressions.

Highlight: The ability to manipulate expressions using index laws is a crucial skill in advanced algebra and calculus.

VIR ya spås (₁) b ху b = = y y Index Laws a+b a-b (add powers) (subtract powers) = = yaxb (multiply powers) worked example m 4 x m 2 3r³ 8 =

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Complex Index Manipulations

The final page presents more advanced applications of the laws of indices, demonstrating their use in complex mathematical expressions.

One example shown is:

m24m^24^9 = m^216

This utilizes the multiplication law of indices, where the exponents are multiplied when a power is raised to another power.

Another example is:

3r23r^2^4 = 81r^8

Example: In this case, we raise both the base number and the variable to the power of 4: 3^4 = 81 and r2r^2^4 = r^8.

These examples showcase how index laws can be applied to solve complex problems involving nested exponents and multiple variables.

Highlight: Mastering these complex manipulations is essential for success in higher-level mathematics courses.

The page also includes additional examples that further reinforce the application of various index laws in different scenarios.

VIR ya spås (₁) b ху b = = y y Index Laws a+b a-b (add powers) (subtract powers) = = yaxb (multiply powers) worked example m 4 x m 2 3r³ 8 =

Sign up to see the contentIt's free!

Access to all documents

Improve your grades

Join milions of students

By signing up you accept Terms of Service and Privacy Policy

Index Laws: Addition and Multiplication

The first page introduces two fundamental laws of indices: the addition law and the multiplication law. These laws are essential for simplifying expressions involving exponents.

Definition: Index laws are rules that govern how to manipulate expressions with exponents.

The page presents three key laws:

  1. Addition of powers: y^a × y^b = y^a+ba+b
  2. Subtraction of powers: y^a ÷ y^b = y^a−ba-b
  3. Multiplication of powers: yay^a^b = y^a×ba×b

Example: Using the addition law, we can simplify x^3 × x^4 to x^7 because 3 + 4 = 7.

These laws form the foundation for more complex operations with indices and are crucial for solving algebraic equations efficiently.

Highlight: The multiplication law of indices is particularly useful in simplifying nested exponents.

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Paul T

iOS user

The app is very easy to use and well designed. I have found everything I was looking for so far and have been able to learn a lot from the presentations! I will definitely use the app for a class assignment! And of course it also helps a lot as an inspiration.

Stefan S

iOS user

This app is really great. There are so many study notes and help [...]. My problem subject is French, for example, and the app has so many options for help. Thanks to this app, I have improved my French. I would recommend it to anyone.

Samantha Klich

Android user

Wow, I am really amazed. I just tried the app because I've seen it advertised many times and was absolutely stunned. This app is THE HELP you want for school and above all, it offers so many things, such as workouts and fact sheets, which have been VERY helpful to me personally.

Anna

iOS user

I think it’s very much worth it and you’ll end up using it a lot once you get the hang of it and even after looking at others notes you can still ask your Artificial intelligence buddy the question and ask to simplify it if you still don’t get it!!! In the end I think it’s worth it 😊👍 ⚠️Also DID I MENTION ITS FREEE YOU DON’T HAVE TO PAY FOR ANYTHING AND STILL GET YOUR GRADES IN PERFECTLY❗️❗️⚠️

Thomas R

iOS user

Knowunity is the BEST app I’ve used in a minute. This is not an ai review or anything this is genuinely coming from a 7th grade student (I know 2011 im young) but dude this app is a 10/10 i have maintained a 3.8 gpa and have plenty of time for gaming. I love it and my mom is just happy I got good grades

Brad T

Android user

Not only did it help me find the answer but it also showed me alternative ways to solve it. I was horrible in math and science but now I have an a in both subjects. Thanks for the help🤍🤍

David K

iOS user

The app's just great! All I have to do is enter the topic in the search bar and I get the response real fast. I don't have to watch 10 YouTube videos to understand something, so I'm saving my time. Highly recommended!

Sudenaz Ocak

Android user

In school I was really bad at maths but thanks to the app, I am doing better now. I am so grateful that you made the app.

Greenlight Bonnie

Android user

I found this app a couple years ago and it has only gotten better since then. I really love it because it can help with written questions and photo questions. Also, it can find study guides that other people have made as well as flashcard sets and practice tests. The free version is also amazing for students who might not be able to afford it. Would 100% recommend

Aubrey

iOS user

Best app if you're in Highschool or Junior high. I have been using this app for 2 school years and it's the best, it's good if you don't have anyone to help you with school work.😋🩷🎀

Marco B

iOS user

THE QUIZES AND FLASHCARDS ARE SO USEFUL AND I LOVE THE SCHOOLGPT. IT ALSO IS LITREALLY LIKE CHATGPT BUT SMARTER!! HELPED ME WITH MY MASCARA PROBLEMS TOO!! AS WELL AS MY REAL SUBJECTS ! DUHHH 😍😁😲🤑💗✨🎀😮

Elisha

iOS user

This app is phenomenal down to the correct info and the various topics you can study! I greatly recommend it for people who struggle with procrastination and those who need homework help. It has been perfectly accurate for world 1 history as far as I’ve seen! Geometry too!

Paul T

iOS user