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

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abi

10/10/2022

Arithmetic

Index Laws

Subjects

Arithmetic

Square & Cube Roots

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

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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
=

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 $3 × 5 × 2 = 30$ and add the exponents of r $3 + 4 + 8 = 15$ .

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.

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 $15 ÷ 3 = 5$ and subtract the exponents $12 - 6 = 6$ .

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.

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:

$m^24$ ^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:

$3r^2$ ^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 $r^2$ ^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

•

10 Oct 2022

•

4 pages

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

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

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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 $3 × 5 × 2 = 30$ and add the exponents of r $3 + 4 + 8 = 15$ .

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.

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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 $15 ÷ 3 = 5$ and subtract the exponents $12 - 6 = 6$ .

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.

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:

$m^24$ ^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:

$3r^2$ ^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 $r^2$ ^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.

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:

Addition of powers: y^a × y^b = y^ $a+b$
Subtraction of powers: y^a ÷ y^b = y^ $a-b$
Multiplication of powers: $y^a$ ^b = y^ $a×b$

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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