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RS Aggarwal Solutions

RS Aggarwal Class 7 Solutions Chapter-5 Exponents

RS Aggarwal Class 7 Solutions Chapter-5 Exponents

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Class 7 RS Aggarwal Chapter-5 Exponents Solutions - Free PDF Download

RS Aggarwal class 7 maths chapter 5 that is Exponents can be easily understood by the learners. Vedantu online learning website has made it possible. Now the student can also download PDF format of the solutions of exponents and powers class 7 chapter 5. To understand more clearly step by step how the question is solved, one can refer to the online video lectures of Vedantu.

Students can also ask their doubts and clear their queries from the experts of Vedantu. In RS Aggarwal class 7 maths chapter 5 is explained in simple language that students can understand. Every NCERT Solution is provided to make the study simple and interesting on Vedantu. You can download NCERT Maths Class 7 and Class 7 Science NCERT Solutions solved by Expert Teachers as per NCERT (CBSE) Book guidelines.F

RS Aggarwal Solutions for Class 7 Maths Chapter 5

Exponents

The exponent of a number indicates how many times we multiply a number by itself. For example, 34 indicates that we have multiplied 3 four times. The expanded form is 3×3×3×3. Exponent is also known as the power of a number. It can be an integer, a fraction, a negative number, or decimals. In this lesson, I will learn more about exponents.

What Exactly are Exponents?

The exponent of a number indicates how many times the number has been multiplied by itself. For instance, 2×2×2×2 can be written as 2^4, because 2 is multiplied by itself four times. In this case, 2 is referred to as the base, and 4 is referred to as the exponent or power. In general, a^m denotes that a has been multiplied by itself m times.

In this case, the term a^m

a is known as the base, and
m is known as the exponent or power.
a to the power of m (or a raised to m) is how a^m is written.

Examples of Exponents

Some of the examples of the exponents are given below:

4×4×4×4×4= 4^5
-4×-4×-4×-4×-4= (-4)^5
b×b×b×b×b= b^5

What is the Significance of Exponents?

Exponents are important because it is difficult to write products where a number is repeated by itself many times without them. For example, it is much easier to write 4^8 than it is to write 4×4×4×4×4×4×4×4

Exponent Properties

To solve problems involving exponents, the properties of exponents or laws of exponents are used. These properties are also known as major exponents rules, which must be followed when solving exponents. The properties of exponents are discussed further below.

Product Law: x^a× x^a = x^a+b
Quotient Law: x^a/x^b = x^a-b
Zero Exponent Law: x⁰ = 1
Negative Exponent Law: x^-a = 1/x^a
Power of a Power Law: (x^a)^b = x^ab
Power of a ProductLaw: (xy)^a = x^ay^a
Power of a Quotient Law: (x/y)^a = x^a/y^a

Negative Exponents

A negative exponent indicates how many times the reciprocal of the base must be multiplied. For example, if it is given that b-a, it can be expanded as 1/ba. That is, we must multiply the reciprocal of b, i.e. 1/b times. When writing fractions with exponents, negative exponents are used. Some of the examples of negative exponents are 4 × 2^-8, 6^-4, 24^-4, etc.

Fractional Exponents

A fractional exponent is the exponent of a number that is a fraction. Square roots, cube roots, and the nth root are all fractional exponents. The square root of a number with power 1/2 is known as the square root of the base. Similarly, a number with a power of one-third is known as the cube root of the base. Fractional exponents include 4^2/5, -6^2/4, 12^4/8, and so on.

Decimal Exponents

When the exponent of a number is given in the decimal form, it is referred to as a decimal exponent. Because evaluating the correct answer of any decimal exponent is slightly difficult, we find the approximate answer in such cases. To solve decimal exponents, first, convert the decimal to fraction form. For example, 4^2.5 can be written as 4^5/2, which can be further simplified to yield the final answer of 32 or -32.

RS Aggarwal Solutions for Class 7 Maths Chapter 5

We have provided step by step solutions for all exercise questions given in the pdf of Class 7 RS Aggarwal Chapter-5 Exponents. All the Exercise questions with solutions in Chapter-5 Exponents are given below:

Exercise (Ex 5A) 5.1

Exercise (Ex 5A) 5.2

Exercise (Ex 5A) 5.3

RS Aggarwal Solutions Class 7 Chapter 5 - Key Highlights

The topics covered in class 7 maths chapter 5 exponents and powers are prepared with proper concepts. There are three exercises in exponents and powers class 7 chapter 5. These exercises consist of a series of questions for the students to solve. The questions are arranged in order from simple to complex.

To know how much they have excelled in the topic, they can solve the CCE test paper given in class 7 maths RS Aggarwal chapter 5.

RS Aggarwal Solutions Class 7 Maths Ch 5 - A complete Overview of Exponents

RS Aggarwal Class 7 solutions chapter 5 is divided into 3 exercises and a CCE test paper is attached to it. In this chapter, you will come to know the meaning of exponent. What are the parts of exponents? You will get to know about the terms Base and Power as well. In this chapter, you will learn the laws of exponents that will help you to solve the sums further.

Laws of Exponents:

Let a and b be real numbers.

Then,

a³ × a² = (a)³ + (a)²

This law states that when two identical numbers are multiplied their powers get added.

a³/a² = (a)³ - (a)²

This means that when two identical numbers are divided their powers get subtracted.

(a³)² = (a)³*²

This means when a number has two powers, both the powers get multiplied.

a³ × b³ = (a × b)³

This means when two different numbers that have the same power are multiplied then both the numbers get multiplied. The power is written at the top right corner as common to the whole operation.

a²/b² = (a/b)²

This means when two different numbers of the same power are divided then the numbers get divided and the power is written at the top right corner as common to the whole operation.

a^0 = 1

This means that for any number whose power is zero, the answer will always be equal to 1.

a^-2 = 1/a²

This means that if the power of a number is negative, it will become positive when we reciprocate the number.

Preparation Tips for RS Aggarwal Solutions Class 7 Maths Chapter 5

To get good scores, firstly you need to clear the basic concept of the terms of the exponent.
Learn all the laws of exponent one by one. Your concept of the laws of exponent will get more clear when you will start applying it.
Solve the questions related to it given in the exercise. Start solving the easy questions and then you will be able to solve a more complex form of it.

Conclusion

The book of RS Aggarwal on maths is appropriate for the students. It is designed in such a way that the students can get the proper knowledge in easy language. Students also come to know how to use the concepts in practical life as well.

Vedantu is the best learning website. Here students can get the explanation of RS Aggarwal solutions class 7 chapter 5. The videos have proved to be useful for the students as the presentation slides are very interactive. Students can also ask their queries one by one and get proper guidance from the expert faculty.

FAQs on RS Aggarwal Class 7 Solutions Chapter-5 Exponents

1. How do the RS Aggarwal Class 7 Solutions for Chapter 5 help in solving problems from all exercises like 5A, 5B, and 5C?

The RS Aggarwal Class 7 Solutions for Exponents provide a complete, step-by-step walkthrough for every single problem in all the exercises, including 5A, 5B, and 5C. Each solution demonstrates the correct method and application of exponent laws, ensuring you understand how to approach different types of questions, from basic simplification to more complex ones involving multiple operations.

2. What is the correct method to simplify a fraction with a negative exponent as explained in RS Aggarwal Chapter 5?

To simplify a fraction with a negative exponent, you should use the reciprocal of the base to make the exponent positive. The rule is (a/b)^-n = (b/a)ⁿ. For example, to solve (2/3)^-2, you would first convert it to (3/2)² and then calculate the result, which is 9/4. This is a fundamental method used to solve many problems in this chapter.

3. How are numbers written in standard form (scientific notation) using exponents in this chapter?

The RS Aggarwal solutions explain how to express very large or small numbers in standard form (k x 10ⁿ) using a clear two-step method:

Step 1: Place a decimal point after the first non-zero digit of the number.
Step 2: Multiply this new decimal number by a power of 10. The exponent (n) will be equal to the number of places the decimal point was moved. The exponent is positive if the decimal moves left (for large numbers) and negative if it moves right (for small numbers).

For instance, 56,700,000 is written as 5.67 x 10⁷.

4. Why is any non-zero number raised to the power of zero equal to 1?

Any non-zero number raised to the power of zero is 1 because of the quotient law of exponents (a^m / aⁿ = a^m-n). Consider the example a^m / a^m. We know that any number divided by itself is 1. Using the exponent law, this is also equal to a^m-m = a⁰. Therefore, a⁰ = 1. The RS Aggarwal solutions use this fundamental principle to solve various simplification problems.

5. How do I apply the laws of exponents when the bases are different but the exponents are the same?

When multiplying or dividing terms with different bases but the same exponent, you combine the bases first and keep the exponent. The rules are:

For multiplication: a^m × b^m = (a × b)^m. For example, 2³ × 5³ = (2 × 5)³ = 10³ = 1000.
For division: a^m ÷ b^m = (a ÷ b)^m. For example, 10⁴ ÷ 5⁴ = (10 ÷ 5)⁴ = 2⁴ = 16.

This technique is crucial for simplifying complex expressions found in the later exercises of the chapter.

6. What is a common mistake when solving problems with negative numbers as a base, like (-3)⁴ vs -3⁴?

A common mistake is confusing the placement of the negative sign. The parentheses are extremely important. The expression (-3)⁴ means (-3) is multiplied by itself four times: (-3) × (-3) × (-3) × (-3) = 81. In contrast, -3⁴ means you calculate 3⁴ first and then apply the negative sign: -(3 × 3 × 3 × 3) = -81. The RS Aggarwal solutions highlight this distinction to ensure calculations are accurate.

7. How can the step-by-step RS Aggarwal solutions help me solve complex problems with multiple exponent laws?

The solutions break down complex problems into manageable steps, showing which law to apply at each stage. For a problem like simplifying [(xᵃ/xᵇ)ᶜ], the solution would first guide you to apply the quotient rule inside the bracket to get [(xᵃ⁻ᵇ)ᶜ], and then apply the power of a power rule to get the final answer xᶜ⁽ᵃ⁻ᵇ⁾. Following this structured approach helps build the logical thinking needed for exams.