Class-7-Maths-Exponents and Powers-Ex 13.1

NCERT Solutions For Class 7 Maths Chapter 13 – Exponents and Powers

Simple solutions for NCERT Solutions for Class 7 Maths Exercise 13.1 Chapter 13 Exponents and Powers are given here in the post. This NCERT Solutions for Class 7 Maths Exercise 13.1 contains topics related to the raw data collection and its organisation. so we definitely want students of Class 7 to solve Class 7 Exponents and Powers NCERT Exercise 13.1 to empower their basics and test the students capability of understanding the concepts. It also helps the students of CBSE Class 7 Maths students

Question 1. Find the value of:

(i) 2⁶

Solution:-

2⁶ = 2 × 2 × 2 × 2 × 2 × 2    = 64

(ii) 9³

Solution:-

9³ = 9 × 9 × 9 = 729

(iii) 11²

Solution:-

11² = 11 × 11 = 121

(iv) 5⁴

Solution:-

5⁴ = 5 × 5 × 5 × 5 = 625

Question 2. Express the following in exponential form:

(i) 6 × 6 × 6 × 6 = 6⁴

(ii) t × t = t²

(iii) b × b × b × b = b⁴.

(iv) 5 × 5× 7 × 7 × 7 = 5² × 7².

(v) 2 × 2 × a × a = 2² × a².

(vi) a × a × a × c × c × c × c × d = a³ × c⁴ × d.

Question 3. Express each of the following numbers using exponential notation:

Solution:-

(i) 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2⁹

(ii) 343 = 7 × 7 × 7= 7³.

(iii) 729 = 3 × 3 × 3 × 3 × 3 × 3= 3⁶.

(iv) 3125 = 5 × 5 × 5 × 5 × 5= 5⁵.

Question 4. Identify the greater number, wherever possible, in each of the following?

(i) 4³ or 3⁴ 

Solution:-

The expansion of 4³ = 4 × 4 × 4 = 64

The expansion of 3⁴ = 3 × 3 × 3 × 3 = 81

Clearly,

64 < 81

So, 4³ < 3⁴ 

Hence 3⁴ is the greater number.

(ii) 5³ or 3⁵

Solution:-

The expansion of 5³ = 5 × 5 × 5 = 125

The expansion of 3⁵ = 3 × 3 × 3 × 3 × 3= 243

125 < 243

So, 5³ < 3⁵

Hence 3⁵ is the greater number.

(iii) 2⁸ or 8²

Solution:-

The expansion of 2⁸ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256

The expansion of 8² = 8 × 8= 64

Clearly,

256 > 64

So, 2⁸ > 8²

Hence 2⁸ is the greater number.

(iv) 100² or 2¹⁰⁰

Solution:-

The expansion of 100² = 100 × 100 = 10000

The expansion of 2¹⁰ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024

(2¹⁰)¹⁰= 1024 × 1024 ×1024 × 1024 ×1024 × 1024 × 1024 × 1024 × 1024 × 1024 =

Clearly,

100² < 2¹⁰⁰

Hence 2¹⁰⁰ is the greater number.

(v) 2¹⁰ or 10²

Solution:-

The expansion of 2¹⁰ = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 1024

The expansion of 10²= 10 × 10= 100

Clearly,

1024 > 100

So, 2¹⁰ > 10²

Hence 2¹⁰ is the greater number.

Question 5. Express each of the following as product of powers of their prime factors:

(i) 648

Solution:-

Factors of 648 = 2 × 2 × 2 × 3 × 3 × 3 × 3 =  2³ × 3⁴ 

(ii) 405

Solution:-

Factors of 405 = 3 × 3 × 3 × 3 × 5= 3⁴ × 5

(iii) 540

Solution:-

Factors of 540 = 2 × 2 × 3 × 3 × 3 × 5 = 2²× 3³× 5

(iv) 3,600

Solution:-

Factors of 3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5 = 2⁴× 3²× 5²

Question 6. Simplify:

(i) 2 × 10³ 

Solution:-

2 × 10³ = 2 × 10 × 10 × 10

= 2 × 1000

= 2000

(ii) 7² × 2²

Solution:-

7² × 2² = 7 × 7 × 2 × 2

= 49 × 4

= 196

(iii) 2³× 5

Solution:-

2³× 5 = 2 × 2 × 2 × 5

= 8 × 5

= 40

(iv) 3 × 4⁴

Solution:-

3 × 4⁴ = 3 × 4 × 4 × 4 × 4

= 3 × 256

= 768

(v) 0 × 10²

Solution:-

0 × 10² = 0 × 10 × 10

= 0 × 100

= 0

(vi) 5² × 3³

Solution:-

5² × 3³ = 5 × 5 × 3 × 3 × 3

= 25 × 27

= 675

(vii) 2⁴ × 3²

Solution:-

2⁴ × 3² = 2 × 2 × 2 × 2 × 3 × 3

= 16 × 9

= 144

(viii) 3² × 10⁴

Solution:-

3² × 10⁴= 3 × 3 × 10 × 10 × 10 × 10

= 9 × 10000

= 90000

Question 7. Simplify:

(i) (– 4)³

Solution:-

The expansion of (– 4)³

= – 4 × – 4 × – 4

= – 64

(ii) (–3) × (–2)³

Solution:-

The expansion of (–3) × (–2)³

= – 3 × – 2 × – 2 × – 2

= – 3 × – 8

= 24

(iii) (–3)² × (–5)²

Solution:-

The expansion of (–3)² × (–5)²

= – 3 × – 3 × – 5 × – 5

= 9 × 25

= 225

(iv) (–2)³ × (–10)³

Solution:-

The expansion of (–2)³ × (–10)³

= – 2 × – 2 × – 2 × – 10 × – 10 × – 10

= – 8 × – 1000

= 8000

Question 8. Compare the following numbers:

(i) 2.7 × 10¹² ; 1.5 × 10⁸

Solution:-

Comparing the exponents of base 10,

Clearly,

2.7 × 10¹² > 1.5 × 10⁸

(ii) 4 × 10¹⁴ ; 3 × 10¹⁷

Solution:-

By observing the question

Comparing the exponents of base 10,

Clearly,

4 × 10¹⁴ < 3 × 10¹⁷