SEBA Class 7 Mathematics Chapter 13 Exponents and Powers

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SEBA Class 7 Mathematics Chapter 13 Exponents and Powers

Also, you can read the SCERT book online in these sections Solutions by Expert Teachers as per SCERT (CBSE) Book guidelines. SEBA Class 7 General Maths Textual Question Answer. These solutions are part of SCERT All Subject Solutions. Here we have given SEBA Class 7 Mathematics Chapter 13 Exponents and Powers Solutions for All Subject, You can practice these here.

Exponents and Powers

Chapter – 13

PART – II

Exercise – 13.1

Q. 1. Find out the correct answer.

(i) The value of (-1)⁵ is:

(a) -1

(b) 1

(c) 5

(d) -5

Ans: (a) -1

(ii) The value of (-5)⁴ is:

(a) -625

(b) 625

(c) 256

(d) -256

Ans: (b) 625

2. Express in exponential form:

(i) 5 × 5 × 5 × 5 × 5

Ans: 5 × 5 × 5 × 5 × 5 = 5⁵

(ii) 3 × 3 × 2 × 2 × 2

Ans: 3 × 3 × 2 × 2 × 2 = 3² × 2³

(iii) (-2) × (-2) × (-2) × 3 × 3 × 3 × 3

Ans: (-2) × (-2) × (-2) × 3 × 3 × 3 × 3 = (-2)³ × 3⁴

(iv) b × b × b × b × b × c × c × c

Ans: b × b × b × b × b × c × c × c = b⁵ × c³

(v) a × a × a × b × b × c × c × c × c × c 

Ans: a × a × a × b × b × c × c × c × c × c = a³ × b² × c⁵

3. Find the value of-

(i) 2⁷

Ans: 2⁷ = 2 × 2 × 2 × 2 × 2 × 2 × 2

= 128

(ii) (-2)⁷

Ans: (-2)⁷ = (-2) × (-2) × (-2) × (-2) × (-2) × (-2) × (-2)

= -128

(iii) 3⁶

Ans: 3⁶ = 3 × 3 × 3 × 3 × 3 × 3

= 729

(iv) (-3)⁶

Ans: (-3)⁶ = (-3) × (-3) × (-3) × (-3) × (-3) × (-3)

= -729

(v) 2⁵ × 4⁴

Ans: 2⁵ × 4⁴ = 2 × 2 × 2 × 2 × 2 × 4 × 4 × 4 × 4

= 32 × 256 

= 8192

(vi) 5² × 3³

Ans: 5² × 3³ = 5 × 5 × 3 × 3 × 3 = 25 × 27

= 675

(vii) (-3)² × (-5)³

Ans: (-3)² × (-5)³ = (-3)² × (-5)³ 

= 9 × (-125)

= -1125

4. Express in exponential form:

(i) 343

Ans: 343

= 7 × 7 × 7

= 7³

(ii) 729

Ans: 729

= 3 × 3 × 3 × 3 × 3 × 3

= 3⁶

(iii) 2187

Ans: 2187

= 3 × 3 × 3 × 3 × 3 × 3 × 3

= 3⁷

(iv) -2187

Ans: -2187

= (-3) × (-3) × (-3) × (-3) × (-3) × (-3) × (-3) 

= (-3)⁷

(v) 3125

Ans: 3125

= 5 × 5 × 5 × 5 × 5

= 5⁵

(vi) -3125

Ans: -3125

= (-5) × (-5) × (-5) × (-5) × (-5) 

= (-5)⁵

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

(i) 100

Ans: 100 = 2² × 5²

(ii) 300

Ans: 300 = 2² × 3 × 5²

(iii) 1000

Ans: 1000 = 2³ × 5³

(iv) 2700

Ans: 2700 = 2² × 5² × 3³

(v) 405

Ans: 405 = 5 × 3⁴

(vi) 1600

Ans: 1600 = 2⁶ × 5²

6. Fill in the blanks with appropriate sign (>, < or =).

Ans: (- 5)³  <  5³

Ans: (-5)² = 5²

Ans: (-7)⁴ = 7⁴

Ans: (-1)¹⁵ < (-1)¹⁰

Ans: (-1)¹¹ < (-1)¹¹

Ans: 2⁷ > 2⁶

7. If 2592 = 2ᵐ × 3ⁿ, then find the value of m and n.

Ans: 2592 = 2ᵐ × 3ⁿ

⇒ 2⁵ × 3⁴ = 2ᵐ = 3ⁿ                                    

∴ m = 5 and n = 4

8. If 16875 = 3ᵐ × 5ⁿ, then find the value of m and n.

Ans: 16875 = 3ᵐ × 5ⁿ 

⇒ 3³ × 5⁴ = 3ᵐ × 5ⁿ 

∴ m = 3 and n = 4

Exercise – 13.2

1. Simplify using laws of exponents (Write the answer in the exponential form)

(i) 3⁵ × 3⁷ × 3¹⁰

Ans: 3⁵ × 3⁷ × 3¹⁰ = 3⁵⁺⁷⁺¹⁰ 

= 3²²

(ii) (2⁷ × 2⁶) ÷ 2⁵

Ans: (2⁷ × 2⁶) ÷ 2⁵ 

= 2⁷⁺⁶ ÷ 2⁵ = 2¹³ ÷ 2⁵ 

= 2¹³⁻⁵ 

= 2⁸

(iii) (2⁰ × 2⁵ × 2⁸) ÷ (2⁰ × 2⁶ × 2⁷)

Ans: (2⁰ × 2⁵ × 2⁸) ÷ (2⁰ × 2⁶ × 2⁷)

= (1 × 2⁵⁺⁸) ÷ (1 × 2⁶⁺⁷)

= 2¹³ ÷ 2¹³ 

= 2¹³⁻¹³

= 2⁰ = 1

(iv) (3⁴)² × (3²)³

Ans: (3⁴)² × (3²)³

= 3⁸ × 3⁶

= 3⁸⁺⁶

= 3¹⁴

(v) (16² × 8³) ÷ (2⁵)²

Ans: (16² × 8³) ÷ (2⁵)²

= {(2⁴)⁷ × (2³)³} ÷ (2¹⁰)

= (2²⁸ × 2⁹) ÷ 2¹⁰

= 2²⁸⁺⁹ ÷ 2¹⁰

= 2³⁷ ÷ 2¹⁰

= 2^37-10

= 2²⁷

Ans: 

Ans: 

Ans: 

Ans:

= 2  × 3 = 6 

Ans: 

Ans: 

2. Express in terms of prime factors and write in exponential form-

(i) 768

Ans: 768 

= 2⁸ × 3

(ii) 729 

Ans: 729 = 3 × 3 × 3 × 3 × 3 × 3 

= 3⁶

(iii) 128 × 625 

Ans: 128 × 625

= 2⁷ ×  5⁴

(iv) 64 × 729 

Ans: 64 × 729 

= 2⁶ × 3⁶

(v) 1000

Ans: 1000 

= 2³ × 5³

3. Simplify:

Ans:

Ans:

Ans:

4. If 3^m = 81, then find the value of m.

Ans: 3ᵐ = 81

⇒ 3ᵐ = 3⁴ 

∵ m = 4

5. Check whether it is true or false.

(i) 3a⁰ = (3a)⁰

Ans: Incorrect.

(ii) 2³ > 3²

Ans: Incorrect.

(iii) (5⁰)⁴  = (5⁴)⁰

Ans: Correct.

(iv) 2³ × 3³ = 6⁵

Ans: Incorrect.

(v) 2⁵/3⁵ = (2/3)⁵⁻⁵

Ans: Incorrect.

(vi) 2⁵ = 5²

Ans: Incorrect.

Exercise – 13.3

1. Express one following numbers in standard form:

(i) 5,273,294

Ans: 5273294 = 5.273294 × 10⁶ 

(ⅱ) 7,10,021

Ans: 710021 = 7.10021 × 10⁵

(iii) 6,400,000

Ans: 6400000 = 6.4 × 10⁶

(iv) 18,129

Ans: 18129 = 1.8129 × 10⁴

(v) 23961,32

Ans: 2396132 = 2.396132 × 10⁶

(vi) 75,000,000,000

Ans: 75000000000 = 7.5 × 10¹⁰

(vii) 70,010,000,000

Ans: 70010000000 = 7.001 × 10¹⁰

(viii) 45026.9

Ans: 45026.9 = 4.50269 × 10⁴

(ix) 3206.19

Ans: 3206.19 = 3.20619 × 10³

(x) 475000000000

Ans: 475000000000 = 4.75 × 10¹¹

2. Express the numbers in following statement in standard form-

(i) Radius of Moon 1737.1 km.

Ans: 1.7371 × 10³ km.

(ii) Radius of Earth 6771000 m.

Ans: 6.7771 × 10⁶ m.

(iii) Distance between Mercury and Venus 50,290,000 km.

Ans: 5.029 × 10⁷ km.

(iv) Distance between Mercury and Jupiter 720,420,000 km.

Ans: 7.2042 × 10⁸

(v) 1 light year = 9,460,700,000,000 km.

Ans: 9.4607 × 10¹²

(vi) 1 Nautical Unit (AU) = 149,600,000 km.

Ans: 1.496 × 10⁸ km.

(vii) Mass of Moon 73490,000,000,000,000,000,000 km.

Ans: 7.349 × 10²² kg.

(viii) Radius of the Sun 695510 km.

Ans: 6.9551 × 10⁵ km.

(ix) There is 1,386,000,000 cubic Kilometer sea water on Earth.

Ans: 1.386 × 10⁹ cu. km

(x) Speed of light in Vacuum 299,792,458 meter/second (approx 3000,000,000 meter/second).

Ans: 2.99792458 × 10⁸ m/sec.

3. Compare (which one is greater)

(i) 57610000000000000; 576000000000000000

Ans: 57610000000000000

= 5.761 × 10⁶ > 5.76 × 10¹⁷

(ii) 343.6 × 10¹⁹; .03436 × 10¹⁷

Ans: 343.6 × 10¹⁰ > 0.03436 × 10¹⁷