CBSE Class 7 Mathematics Chapter 13: Exponents and Powers NCERT Solutions

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NCERT Solutions PDF Class 7 PDF

CBSE Class 7 Mathematics Chapter 13, Exponents and Powers, introduces students to the fascinating world of representing large numbers concisely. This chapter delves into understanding what exponents and powers are, how to calculate them, and how to express numbers in exponential form. The NCERT Solutions provide clear, step-by-step explanations for all the exercises, ensuring students can easily follow along and build a strong foundation. We explore concepts like base, exponent, and how to multiply powers with the same base. These solutions are designed to help students not only solve problems accurately but also develop a deeper comprehension of the underlying mathematical principles, making them well-prepared for exams.

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BoardCBSE
ClassClass 7
SubjectMathematics
Session2026
LanguageEnglish
TypeNCERT Solutions
ChapterChapter 13: Exponents and Powers

Chapter summary

Chapter 13, Exponents and Powers, for Class 7 Mathematics focuses on introducing students to the concept of representing numbers using exponents. The NCERT Solutions for this chapter provide detailed explanations and step-by-step solutions for exercises that involve calculating the values of expressions with exponents and converting expanded forms into exponential notation. Students will learn to identify the base and exponent and apply them to simplify and represent numbers efficiently.

Learning outcomes

  • Understand the concept of exponents and powers.
  • Calculate the value of expressions involving exponents.
  • Express numbers in exponential form.
  • Identify the base and exponent in a given power.
  • Solve problems related to multiplication of numbers in expanded form.

Topics covered

Paper topics

  • Exponents
  • Powers
  • Base
  • Exponent
  • Exponential form
  • Calculating values of powers
  • Prime factorization
  • Representing numbers in exponential notation

Important topics

  • Understanding exponential notation ($a^n$)
  • Calculating the value of $a^n$
  • Converting expanded form to exponential form
  • Converting numbers to exponential form using prime factorization

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Questions and Solutions

Question 1

Find the value of: (i) $2^6$ (ii) $9^3$ (iii) $11^2$ (iv) $5^4$
Solution:

To find the value of these expressions, we need to multiply the base by itself the number of times indicated by the exponent.

  1. For $2^6$, the base is 2 and the exponent is 6. This means we multiply 2 by itself 6 times:

    2^6 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 64

  2. For $9^3$, the base is 9 and the exponent is 3. This means we multiply 9 by itself 3 times:

    9^3 = 9 \times 9 \times 9 = 729

  3. For $11^2$, the base is 11 and the exponent is 2. This means we multiply 11 by itself 2 times:

    11^2 = 11 \times 11 = 121

  4. For $5^4$, the base is 5 and the exponent is 4. This means we multiply 5 by itself 4 times:

    5^4 = 5 \times 5 \times 5 \times 5 = 625

Question 2

Express the following in exponential form: (i) $6 \times 6 \times 6 \times 6$ (ii) $t \times t$ (iii) $b \times b \times b \times b$ (iv) $5 \times 5 \times 7 \times 7 \times 7$ (v) $2 \times 2 \times a \times a$ (vi) $a \times a \times a \times c \times c \times c \times c \times d$
Solution:

To express these in exponential form, we count how many times each factor appears and write it as a base raised to that count (the exponent).

  1. The number 6 appears 4 times. So, the exponential form is:

    6 \times 6 \times 6 \times 6 = 6^4

  2. The variable $t$ appears 2 times. So, the exponential form is:

    t \times t = t^2

  3. The variable $b$ appears 4 times. So, the exponential form is:

    b \times b \times b \times b = b^4

  4. The number 5 appears 2 times, and the number 7 appears 3 times. So, the exponential form is:

    5 \times 5 \times 7 \times 7 \times 7 = 5^2 \times 7^3

  5. The number 2 appears 2 times, and the variable $a$ appears 2 times. So, the exponential form is:

    2 \times 2 \times a \times a = 2^2 \times a^2

  6. The variable $a$ appears 3 times, the variable $c$ appears 4 times, and the variable $d$ appears 1 time. So, the exponential form is:

    a \times a \times a \times c \times c \times c \times c \times d = a^3 \times c^4 \times d^1 = a^3 c^4 d

Question 3

Express each of the following numbers using exponential notation: (i) 512 (ii) 343 (iii) 729 (iv) 3125
Solution:

To express these numbers in exponential notation, we find their prime factorization and then write the factors in exponential form.

  1. For 512: We find the prime factors of 512.

    512 = $2 \times 256$

    256 = $2 \times 128$

    128 = $2 \times 64$

    64 = $2 \times 32$

    32 = $2 \times 16$

    16 = $2 \times 8$

    8 = $2 \times 4$

    4 = $2 \times 2$

    2 = $2 \times 1$

    So, 512 has nine factors of 2. The exponential notation is:

    512 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 = 2^9

  2. For 343: We find the prime factors of 343.

    343 = $7 \times 49$

    49 = $7 \times 7$

    7 = $7 \times 1$

    So, 343 has three factors of 7. The exponential notation is:

    343 = 7 \times 7 \times 7 = 7^3

  3. For 729: We find the prime factors of 729.

    729 = $3 \times 243$

    243 = $3 \times 81$

    81 = $3 \times 27$

    27 = $3 \times 9$

    9 = $3 \times 3$

    3 = $3 \times 1$

    So, 729 has six factors of 3. The exponential notation is:

    729 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 3^6

    (Note: The source incorrectly stated $3^6 = 36$. The correct value is $3^6 = 729$.)

  4. For 3125: We find the prime factors of 3125.

    3125 = $5 \times 625$

    625 = $5 \times 125$

    125 = $5 \times 25$

    25 = $5 \times 5$

    5 = $5 \times 1$

    So, 3125 has five factors of 5. The exponential notation is:

    3125 = 5 \times 5 \times 5 \times 5 \times 5 = 5^5

Common mistakes

  • Confusing the base and the exponent.
  • Incorrectly calculating the value of powers, especially with negative bases (though not present in this specific exercise).
  • Errors in prime factorization when converting numbers to exponential form.
  • Misapplying the rules of exponents (though rules are not explicitly tested in this exercise).

Revision tips

  • Practice calculating powers of small numbers manually to build intuition.
  • Ensure you understand the difference between $a^n$ and $a \times n$.
  • Review the prime factorization method for converting numbers into exponential notation.
  • Work through each example and exercise problem to solidify understanding.

Practice MCQs

Q1. What is the value of $2^6$?

Q2. Express $6 \times 6 \times 6 \times 6$ in exponential form.

Q3. What is the base in the expression $7^3$?

Q4. The exponential form of $5 \times 5 \times 7 \times 7 \times 7$ is:

Q5. What is the value of $11^2$?

Frequently asked questions

What is the main concept covered in Chapter 13 of Class 7 Maths?

Chapter 13, Exponents and Powers, introduces students to the concept of representing numbers using exponents, where a number is multiplied by itself a certain number of times. It covers how to write numbers in exponential form and calculate their values.

How do these NCERT Solutions help students?

These solutions provide clear, step-by-step explanations for each problem in Exercise 13.1. They help students understand the process of calculating powers and converting numbers into exponential notation, reinforcing their learning.

What is the difference between a base and an exponent?

In an expression like $a^n$, 'a' is called the base, which is the number being multiplied, and 'n' is called the exponent, which indicates how many times the base is multiplied by itself.

How can I express a number like 512 in exponential form using these solutions?

You can express 512 in exponential form by finding its prime factors. As shown in the solutions, 512 can be repeatedly divided by 2 until you reach 1. Counting the number of 2s (which is 9), you get the exponential form $2^9$.

Are these solutions useful for exam preparation?

Yes, these solutions are very useful for exam preparation. They cover the core concepts and problem-solving techniques required for the Exponents and Powers chapter, allowing students to practice and revise effectively.

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