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Exponents indicate how many times a number, called the base, is multiplied by itself.
How do you handle exponents with different bases?
You cannot directly add or subtract numbers with different bases and exponents. You can only combine them through multiplication or division if they have the same base or use the rules for exponents to simplify expressions.
What is scientific notation, and how does it use exponents?
Scientific notation expresses very large or very small numbers as a product of a number between 1 and 10 and a power of 10.
How do you solve equations involving exponents?
To solve equations with exponents, you might need to apply logarithms, use the laws of exponents to simplify, or solve for the exponent by isolating it.
CBSE Class 8 Maths Notes Chapter 10 Exponents and Powers
Here we have provided CBSE Class 8 Maths Notes Chapter 10 Exponents and Powers for the ease of students so that they can prepare better for their exams.
Ananya Gupta23 Aug, 2024
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CBSE Class 8 Maths Notes Chapter 10:
CBSE Class 8 Maths Chapter 10 Exponents and Powers explain the fundamental concepts of exponents, which represent repeated multiplication of a number by itself.
The chapter introduces the laws of exponents, including multiplication and division rules, as well as the power of a power rule. It covers how to handle zero and negative exponents and explains the significance of scientific notation for representing large or small numbers succinctly.
Through clear examples and practice problems students learn to simplify expressions involving exponents and understand their applications in various mathematical contexts.
CBSE Class 8 Maths Notes Chapter 10 Exponents and Powers Overview
These notes, prepared by subject experts at Physics Wallah provide a detailed overview of CBSE Class 8 Maths Chapter 10 Exponents and Powers.It explains how exponents represent repeated multiplication and covers key concepts such as the laws of exponents, including multiplication, division, and the power of a power.
With detailed explanations and practical examples, these notes aim to simplify complex topics and enhance students' understanding of exponents and their applications in
CBSE Class 8 Maths Notes Chapter 10 Exponents and Powers
This chapter introduces students to the fundamental concepts of exponents and powers, providing a clear understanding of how to work with these mathematical tools. It covers the definition of exponents, explaining how an exponent indicates the number of times a base is multiplied by itself.
The chapter outlines the key laws of exponents, including the product of powers, quotient of powers, and power of a power, which help in simplifying expressions involving exponents. Students will learn how to handle various types of exponents, including zero, negative, and fractional exponents.
The notes also include practical examples and problems to reinforce these concepts, helping students apply their knowledge effectively in solving equations and simplifying expressions. With clear explanations and numerous practice exercises these notes aim to build a strong foundation in exponents and powers, crucial for mastering more advanced mathematical topics.
Powers and Exponents
Powers and exponents
are fundamental concepts in mathematics used to simplify the expression of repeated multiplication. When a number is raised to a power, it shows how many times to multiply that number (called the base) by itself.
For example: Consider 9³. Here the exponent ‘3’ indicates that base ‘9’ needs to be multiplied three times to get our equivalent answer which is 729.
Powers with Negative Exponents
Powers with negative exponents represent the reciprocal of the base raised to the positive exponent. When a number has a negative exponent, it means you take the reciprocal of the base and then raise it to the positive version of that exponent.
For instance, a base with a negative exponent can be rewritten as the reciprocal of the base raised to the corresponding positive exponent. This helps in simplifying expressions by converting negative exponents into a more manageable reciprocal form.
In simple terms, for a non-zero integer a with an exponent -b, a-b = 1/ab
Expanding a Rational Number Using Powers
To write the number 1204.65 in expanded form using exponents, it is:
1204.65=1000+200+4+0.6+0.05=(1×10³)+(2×10²)+(0×10¹)+(4×10
-1
)+(5×10
-2
)
Laws of Exponents
Exponents with like Bases
Given a non-zero integer a, a
m
×a
n
=a
m+n
where m and n are integers.
and a
m
÷a
n
=a
m−n
where m and n are integers.
For example: 2
3
×2
7
= 2
7 + 3
= 2
10
and 2
7
/2
3
= 2
7−3
Power of a Power
Given a non-zero integer a, (a
m
)
n
= a
mn
, where m and n are integers.
For example: (2
4
)
3
= 2
4×3
= 2
12
Given a non-zero integer a,
(a)
0
= 1 Any number to the power 0 is always 1.
Exponents with Unlike Bases and Same Exponent
Given two non-zero integers a and b,
a
m
×b
m
= (a×b)
m
, where m is an integer.
For example: 2
3
×5
3
= (2×5)
3
= 10
3
= 1000
Uses of Exponents
Inter Conversion between Standard and Normal Forms
Very
large numbers
or very
small numbers
can be represented in the
standard form
with the help of
exponents
.
If it is a very large number like 150,000,000,000, then we need to move the
decimal place towards the left
. And when we do so the exponent will be
positive.
Since the
decimal
is moved
11 places
till it is placed between 1 and 5, our standard form representation of the large number will be 1.5×10
11
If it is a very small number like 0.000007, we need to move the
decimal places to the right
in order to represent the number in its standard form. When being shifted to the right, the exponent will be
negative.
In this case, the decimal place is moved
6
places up until it is placed after digit 7. Therefore our standard form representation will be
7×10
−6
The exponents are also useful when converting the number from it’s standard form to it’s natural form.
Comparison of Quantities Using Exponents
In order to
compare two large or small quantities
, we convert them to their standard exponential form and divide them.
For example : To compare the diameter of the earth and that of the sun.
Diameter of the Earth = 1.2756 × 10
6
m
Diameter of the Sun =1.4×10
9
m
Diameter of the Earth = 1.4×10
9
m
1.2756 × 10
7
m=109
When calculating the total or difference between two quantities in scientific notation or with exponents, it's essential to ensure that the exponents are the same.
CBSE Class 8 Maths Notes Chapter 10 PDF Download
The PDF for CBSE Class 8 Maths Notes Chapter 10 Exponents and Powers is available for download below. This chapter focuses on the fundamental concepts of exponents, which are crucial for understanding how powers and roots work in mathematics. It covers topics such as the basic rules of exponents, including multiplication and division of powers, as well as how to handle zero and negative exponents.
The notes also introduce scientific notation, providing a clear and practical approach to dealing with very large or very small numbers. These comprehensive notes are designed to help students grasp the key principles of exponents and powers, making complex mathematical operations more accessible and manageable.
Benefits of CBSE Class 8 Maths Notes Chapter 10 Exponents and Powers
Concept Clarity:
Provides clear explanations of fundamental concepts, including definitions and rules of exponents and powers, helping students understand the topic thoroughly.
Simplified Learning:
Breaks down complex topics into manageable parts, making it easier for students to grasp and apply the concepts.
Step-by-Step Solutions:
Includes detailed solutions and step-by-step methods for solving problems, which helps in reinforcing learning and improving problem-solving skills.
Formulae and Rules:
Summarizes essential formulae, laws of exponents, and rules in a concise manner, making it easy for students to refer to them when needed.
Enhanced Confidence:
Builds confidence in students by providing a structured approach to studying and mastering the chapter, leading to better performance in tests and exams.
Preparation for Advanced Topics:
Lays a strong foundation for more advanced mathematical topics involving exponents and powers, which are essential for higher-level mathematics.
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Since the
decimal
is moved
11 places
till it is placed between 1 and 5, our standard form representation of the large number will be 1.5×10
11
If it is a very small number like 0.000007, we need to move the
decimal places to the right
in order to represent the number in its standard form. When being shifted to the right, the exponent will be
negative.
In this case, the decimal place is moved
6
places up until it is placed after digit 7. Therefore our standard form representation will be
7×10
−6
The exponents are also useful when converting the number from it’s standard form to it’s natural form.
