### NCERT Solutions Class 7 Maths Chapter 11 Exponents and Powers Exercise 11.1

## Introduction:

In this chapter, Exponents and Power we will learn that very large numbers are difficult to read, understand and compare, we use exponents.

We can write large numbers in a shorter form using Exponents.

For example - 10,000 = 10×10×10×10 = 10^{4}

The short notation 10^{4 }stands for the product 10×10×10×10. Here, '10' is called the **base **and '4' the **exponent. The number 10 ^{4} is read as 10 raised to the power of 4 **or simply as

**fourth power of 10.**is called the

**exponential form**of 10,000.

NCERT Class 7 Maths Chapter 11 Exponents and Powers Exercise 11.1

NCERT Class 7 Maths Chapter 11 Exponents and Powers Exercise 11.2

NCERT Class 7 Maths Chapter 11 Exponents and Powers Exercise 11.3

**Class 7 Maths Exercise 11.1 (Page-173)**

**Q1. **Find the value of :

(i) \(\displaystyle {{2}^{6}}\)

(ii) 9³

(iii) 11²

(iv) \(\displaystyle {{5}^{4}}\)

**Solution: **

**(i) **2×2×2×2×2×2 = 64

**(ii) **9×9×9 = 729

**(iii) **11×11 = 121

**(iv) **5×5×5×5 = 625

**Q2. **Exress the following in exponential form:

(i) 6 × 6 × 6 × 6

(ii) t × t

(iii) b × b × b × b

(iv) 5 × 5 × 7 × 7 × 7

(v) 2 × 2 × a × a

(vi) a × a × a × c × c × c× c × d

**Solution: **

**(i) **\(\displaystyle {{6}^{4}}\)

**(ii) **\(\displaystyle {{t}^{2}}\)

**(iii) **\(\displaystyle {{b}^{4}}\)

**(iv) **\(\displaystyle {{5}^{2}}\) × \(\displaystyle {{7}^{3}}\)

**(v) **\(\displaystyle {{2}^{2}}\) × \(\displaystyle {{a}^{2}}\)

**(vi) **\(\displaystyle {{a}^{3}}\) × \(\displaystyle {{c}^{4}}\) × d¹

**Q3. **Express each of the following numbers using exponential notation:

(i) 512

(ii) 343

(iii) 729

(iv) 3125

**Solution: (i) **

2 ×2×2×2×2×2×2×2×2 = \(\displaystyle {{2}^{9}}\)

**(ii) **

7 × 7× 7 = 7³

**(iii) **

3×3×3×3×3×3 = \(\displaystyle {{3}^{6}}\)

**(iv) **

5×5×5×5×5 = \(\displaystyle {{5}^{5}}\)

**Q4. **Identify the greater number, wherever possible, in each of the following?

(i) 4^{3} or 3^{4}

(ii) 5^{3} or 3^{5}

(iii) 2^{8 }or 8^{2}

(iv) 100² or 2^{100}

(v)2^{10 }or 10^{2}

**Solution: **

**(i) **4³ = 4×4×4 = 64

3^{4}= 3×3×3×3= 81

= 64< 81.
Hence, 3^{4 }is a greater number.

**ii) **5³ = 5×5×5 = 125

3^{5} = 3×3×3×3×3 = 243

= 125< 243
Hence, 3^{5} is greater number.

**iii) **2^{8 }= 2×2×2×2×2×2×2×2 = 256

8^{2 }= 8×8 = 64

= 256> 64

Hence, ** 2 ^{8 } **is greater number.

**(iv) **100² = 100×100 = 10000

2^{100}= splitting 2^{100 }into 2^{10}

2^{10 }= 2×2×2×2×2×2×2×2×2×2= 1024

s0, 2^{100 }= 1024×1024×1024×1024×1024×1024×1024×1024×1024×1024

so, ** **100²<2^{100 }

Hence, 2^{100 } is greater number.

**(v) ** 2^{10}= 2×2×2×2×2×2×2×2×2×2= 1024

10²= 10×10= 100

1024> 100

hence, 2^{10} is greater number.

**Q5. **Express each of the following as product of powers of their prime factors:

(i) 648

(ii) 405

(iii) 540

(iv) 3600

**Solution: **

**(i) **648

648 = 2×2×2×3×3×3×3

= 2³× \(\displaystyle {{3}^{4}}\)

**ii) **405

405 = 3×3×3×3×5

405 = \(\displaystyle {{3}^{4}}\)

**iii) **540

540 = 2×2×3×3×3×5

540= 2² × 3³ × 5

**iv) **3600

3600 = 2×2×2×2×3×3×5×5

3600= \(\displaystyle {{2}^{4}}\) × 3² × 5²

**Q6. **Simplify:

(i) 2 × 10³

(ii) 7² × 2²

(iii) 2³ × 5

(iv) 3 × \(\displaystyle {{4}^{4}}\)

(v) 0 ×10²

(vi) 5² × 3³

(vii) \(\displaystyle {{2}^{4}}\) × 3²

(viii) 3² × \(\displaystyle {{10}^{4}}\)

**Solution: **

**i) **2 × 10× 10× 10= 2× 1000

= 2000

**ii) **7×7×2×2

= 49×4

= 196

**iii) **2×2×2×5

= 8×5

= 40

**iv) **3×4×4×4×4

= 3×16×16

= 48×16

= 768

**v) **0( if we multiply any number to zero answer will remain zero)

**vi) **5×5×3×3×3

= 25×27

= 675

**vii) **2×2×2×2×3×3

= 4×4×9

= 16×9

= 144

**viii)** 3×3×10×10×10×10

= 9× 10000

= 90000

**Q7. **Simplify:

(i) (-4)³

(ii) (-3)×(-2)³

(iii) (-3)²× (-5)²

(iv) (-2)³× (-10)³

**Solution: **

**i) ** -4×-4×-4

= 16 ×-4

= - 64

**ii) **(-3) × -2 ×-2×-2

= (-3 )×(-8)

= 24

**iii) **-3×-3×-5×-5

= 9×25

= 225

**(iv) **-2×-2×-2×-10×-10×-10

= -8)×(-1000)

= 8000

**Q8. **Compare the following numbers:

(i) 2.7 × 10^{12} ; 1.5× 10^{8}

(ii) 4× 10^{14}; 3× 10^{17}

**Solution: **

**i) ** 10^{12} >10^{8}

So, 2.7 × 10^{12} > 1.5× 10^{8}

**ii) **10^{14}< 10^{17}

So, 4× 10^{14} <3× 10^{17}