SEBA Class 7 Mathematics Chapter 13 Exponents and Powers Solutions English Medium, SEBA Class 7 Maths Notes in English Medium, SEBA Class 7 Mathematics Chapter 13 Exponents and Powers Notes to each chapter is provided in the list so that you can easily browse throughout different chapter Assam Board SEBA Class 7 Mathematics Chapter 13 Exponents and Powers Solutions in English and select needs one.
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
= 237-10
= 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 3m = 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
Hi, I’m Dev Kirtonia, Founder & CEO of Dev Library. A website that provides all SCERT, NCERT 3 to 12, and BA, B.com, B.Sc, and Computer Science with Post Graduate Notes & Suggestions, Novel, eBooks, Biography, Quotes, Study Materials, and more.
