Exponents and Powersv - Solutions
CBSE Class –VII Mathematics
NCERT Solutions
Chapter 13 Exponents and Powers (Ex. 13.1)
Question 1. Find the value of:
(i) 26 (ii)93 (iii)112 (iv) 54
Answer: (i) 26 = 2 x 2 x 2 x 2 x 2 x 2 = 64
(ii) 93 = 9 x 9 x 9 = 729
(iii) 112 = 11 x 11 = 121
(iv) 54 = 5 x 5 x 5 x 5 = 625
Question 2.Express the following in exponential form:
(i) 6 x 6 x 6 x 6 (ii) t x t (iii) b x b x b x b
(iv) 5 x 5 x 7 x 7 x 7 (v) 2 x 2 x a x a
(vi) a x a x a x c x c x c x c x d
Answer: (i) 6 x 6 x 6 x 6 = 64 (ii) t x t = t2 (iii) b x b x b x b = b4
(iv) 5 x 5 x 7 x 7 x 7 = 52 x 73 (v) 2 x 2 x a x a = 22 x a2
(vi) a x a x a x c x c x c x c x d = a3 x c4 x d
Question 3. Express each of the following numbers using exponential notation:
(i) 512 (ii) 343 (iii) 729 (iv) 3125
Answer: (i) 512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 29
(ii) 343 = 7 x 7 x 7 = 73
(iii) 729 = 3 x 3 x 3 x 3 x 3 x 3 = 36
(iv) 3125 = 5 x 5 x 5 x 5 x 5 = 55
Question 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
Answer: (i) 43= 4 x 4 x 4 = 64
34= 3 x 3 x 3 x 3 = 81
Since 64 < 81
Thus, 34 is greater than 43.
(ii) = 5 x 5 x 5 = 125
= 3 x 3 x 3 x 3 x 3 = 243
Since, 125 < 243
Thus, is greater than .
(iii) = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256
= 8 x 8 = 64
Since, 256 > 64
Thus, is greater than.
(iv) = 100 x 100 = 10,000
= 2 x 2 x 2 x 2 x 2 x …..14 times x ……… x 2 = 16,384 x ….. x 2
Since, 10,000 < 16,384 x ……. X 2
Thus, is greater than.
(v) = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1,024
= 10 x 10 = 100
Since, 1,024 > 100
Thus, >
Question 5. Express each of the following as product of powers of their prime factors:
(i) 648 (ii) 405 (iii) 540 (iv) 3,600
Answer: (i) 648 =
(ii) 405 =
(iii) 540 =
(iv) 3,600 =
Question 6. Simplify:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
(viii)
Answer: (i) = 2 x 10 x 10 x 10 = 2,000
(ii) = 7 x 7 x 2 x 2 = 196
(iii) = 2 x 2 x 2 x 5 = 40
(iv) = 3 x 4 x 4 x 4 x 4 = 768
(v) = 0 x 10 x 10 = 0
(vi) = 5 x 5 x 3 x 3 x 3 = 675
(vii) = 2 x 2 x 2 x 2 x 3 x 3 = 144
(viii) = 3 x 3 x 10 x 10 x 10 x 10 = 90,000
Question 7. Simplify:
(i) (-4)3
(ii)
(iii)
(iv)
Answer: (i)
(ii)
(iii)
(iv)
Question 8. Compare the following numbers:
(i) ;
(ii) ;
Answer: (i) and
On comparing the exponents of base 10,
>
(ii) and
On comparing the exponents of base 10,
<