NCERT MATHS CLASS 7
Chapter 13 Exponents and Powers
अध्याय 13 घातांक और घात
LINK TO SOLUTIONS OF ALL QUESTIONS IS GIVEN BELOW
सभी प्रश्नों के समाधान का लिंक नीचे दिया गया है
We can write large numbers in a shorter form using
exponents.
Observe 10, 000 = 10 × 10 × 10 × 10 = 104
The short notation 104 stands for the
product 10×10×10×10.
Here ‘10’ is
called the base and ‘4’ the exponent.
The number 104 is read as 10 raised to the
power of 4 or simply as fourth power of 10.
104 is called the exponential form of
10,000.
We can similarly express 1,000 as a power of 10.
Note that 1000 = 10 × 10 × 10 = 103
Here again, 103 is the exponential form of 1,000.
Similarly, 1,00,000 = 10 × 10 × 10 × 10 × 10 = 105
105 is the exponential form of 1,00,000 In
both these examples, the base is 10; in case of 103 , the exponent
is 3 and in case of 105 the exponent is 5. Chapter
Multiplying Powers with the Same Base समान आधार से घातों को गुणा करना
For any
non-zero integer a, where m and n are whole numbers, am × an
= am + n
Dividing Powers with the Same Base
For any
non-zero integer a, am ÷ an = am – n
where m and n are whole numbers and m > n.
Taking Power of a Power
For any non-zero
integer ‘a’, where ‘m’ and ‘n’ are whole numbers, (am)n = amn
Multiplying Powers with the Same Exponents
For any
non-zero integer a, am × bm = (ab)m
Dividing Powers with the Same Exponents
am÷ bm = am/bm = (a/b)m where a and b are any non-zero integers and m is a whole number.
Numbers with exponent zero
a 0 = 1 (for any non-zero integer a)
any number (except 0) raised to the power (or
exponent) 0 is 1.
1. Using laws of exponents, simplify and write the answer in exponential form:
(i) 32 × 34 × 38
(ii) 615 ÷ 610
(iii) a3 × a2
(iv) 7x×72
(v) (52 )3 ÷ 53
(vi) 25 × 55
(vii) a4 × b4
(viii) (34 )3
(ix) (220 ÷215) × 23
(x) 8t ÷ 82
3. Say true or false and justify your answer:
(i) 10 × 1011 = 10011
(ii) 23 > 52
(iii) 23 × 32 = 65
(iv) 30 = (1000)0
4. Express each of the following as a product of prime factors only in exponential form: (i) 108 × 192 (ii) 270 (iii) 729 × 64 (iv) 768
DECIMAL NUMBER SYSTEM
These numbers are not convenient to write and read. To
make it convenient we use powers.
1. Sun is located 300,000,000,000,000,000,000 m from
the centre of our Milky Way Galaxy.
300,000,000,000,000,000,000 m can be written as 3.0 ×
100,000,000,000,000,000,000 = 3.0 × 1020 m
2. Number of stars in our Galaxy is 100,000,000,000.
100,000,000,000
= 1×1011
3. Mass of the Earth is
5,976,000,000,000,000,000,000,000 kg.
Mass of the Earth = 5,976,000,000,000,000,000,000,000
kg = 5.976 × 1024 kg
EXERCISE 13.3
1. Write the following numbers in the expanded forms: 279404, 3006194, 2806196, 120719, 20068 2. Find the number from each of the following expanded forms:
(a) 8 ×104 + 6 ×103 + 0×102 + 4×101 + 5×100
(b) 4 ×105 + 5×103 + 3×102 + 2×100
(c) 3 ×104 + 7×102 + 5×100
(d) 9 ×105 + 2×102 + 3×101
3. Express the following numbers in standard form:
(i) 5,00,00,000
(ii) 70,00,000
(iii) 3,18,65,00,000
(iv) 3,90,878
(v) 39087.8
(vi) 3908.78
4. Express the number appearing in the following statements in standard form.
(a) The distance between Earth and Moon is 384,000,000 m.
(b) Speed of light in vacuum is 300,000,000 m/s.
(c) Diameter of the Earth is 1,27,56,000 m.
(d) Diameter of the Sun is 1,400,000,000 m.
(e) In a galaxy there are on an average 100,000,000,000 stars.
(f) The universe is estimated to be about 12,000,000,000 years old.
(g) The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be 300,000,000,000,000,000,000 m.
(h) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.
(i) The earth has 1,353,000,000 cubic km of sea water.
(j) The population of India was about 1,027,000,000 in March, 2001.
EXERCISE 13.1
1. Find the value of: (i) 26 (ii) 93 (iii) 112 (iv) 54
2. Express 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
3. Express each of the following numbers using exponential notations:
(i) 512 (ii) 343 (iii) 729 (iv) 3125
4. Identify the greater number, wherever possible, in each of the following? (i) 43 or 34 (ii) 53 or 35 (iii) 28 or 82 (iv) 1002 or 2100 (v) 210 or 102
5. Express each of the following as product of powers of their prime factors: (i) 648 (ii) 405 (iii) 540 (iv) 3,600
6. Simplify: (i) 2 × 103 (ii) 72 × 22 (iii) 23 × 5 (iv) 3 × 44 (v) 0 × 102 (vi) 52 × 33 (vii) 24 × 32 (viii) 32 × 104
7. Simplify: (i) (– 4)3 (ii)
(–3) × (–2)3 (iii) (–3)2 × (–5)2 (iv) (–2)3
× (–10)3
8. Compare the following numbers: (i) 2.7 ×
1012 ; 1.5 × 108 (ii) 4 × 1014 ; 3 × 1017
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