Exponents and Powers - Solutions 1

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) 2= 2 x 2 x 2 x 2 x 2 x 2 = 64
(ii) 9= 9 x 9 x 9 = 729
(iii) 11= 11 x 11 = 121
(iv) 5= 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) 4or 34
(ii) 5or 35
(iii) 2or 82
(iv) 100or 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, 3is greater than 43.
(ii) ${5}^{3}$= 5 x 5 x 5 = 125
${3}^{5}$= 3 x 3 x 3 x 3 x 3 = 243
Since, 125 < 243
Thus, ${3}^{4}$ is greater than ${5}^{3}$.
(iii) ${2}^{8}$= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 256
${8}^{2}$= 8 x 8 = 64
Since, 256 > 64
Thus, ${2}^{8}$is greater than${8}^{2}$.
(iv) ${100}^{2}$= 100 x 100 = 10,000
${2}^{100}$= 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, ${2}^{100}$is greater than${100}^{2}$.
(v) ${2}^{10}$= 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 = 1,024
${10}^{2}$= 10 x 10 = 100
Since, 1,024 > 100
Thus, ${2}^{10}$${10}^{2}$
Question 5. Express each of the following as product of powers of their prime factors:
(i) 648   (ii) 405    (iii) 540    (iv) 3,600
Answer: (i) 648 = ${2}^{3}×{3}^{4}$
(ii) 405 = $5×{3}^{4}$
(iii) 540 = ${2}^{2}×{3}^{3}×5$
(iv) 3,600 = ${2}^{4}×{3}^{2}×{5}^{2}$
Question 6. Simplify:
(i) $2×{10}^{3}$
(ii) ${7}^{2}×{2}^{2}$
(iii)${2}^{3}×5$
(iv) $3×{4}^{4}$
(v)$0×{10}^{2}$
(vi) ${5}^{2}×{3}^{3}$
(vii)${2}^{4}×{63}^{2}$
(viii) ${3}^{2}×{10}^{4}$
Answer: (i) $2×{10}^{3}$= 2 x 10 x 10 x 10 = 2,000
(ii) ${7}^{2}×{2}^{2}$= 7 x 7 x 2 x 2 = 196
(iii) ${2}^{3}×5$= 2 x 2 x 2 x 5 = 40
(iv) $3×{4}^{4}$= 3 x 4 x 4 x 4 x 4 = 768
(v) $0×{10}^{2}$= 0 x 10 x 10 = 0
(vi) ${5}^{2}×{3}^{3}$= 5 x 5 x 3 x 3 x 3 = 675
(vii) ${2}^{4}×{63}^{2}$= 2 x 2 x 2 x 2 x 3 x 3 = 144
(viii) ${3}^{2}×{10}^{4}$= 3 x 3 x 10 x 10 x 10 x 10 = 90,000
Question 7. Simplify:
(i) (-4)3
(ii) $\left(-3\right)×{\left(-2\right)}^{3}$
(iii) ${\left(-3\right)}^{2}×{\left(-5\right)}^{2}$
(iv) ${\left(-2\right)}^{3}×{\left(-10\right)}^{3}$
Answer: (i) ${\left(-4\right)}^{3}=\left(-4\right)×\left(-4\right)×\left(-4\right)=-64$
(ii) $\left(-3\right)×{\left(-2\right)}^{3}=\left(-3\right)×\left(-2\right)×\left(-2\right)×\left(-2\right)=24$
(iii) ${\left(-3\right)}^{2}×{\left(-5\right)}^{2}=\left(-3\right)×\left(-3\right)×\left(-5\right)×\left(-5\right)=225$
(iv) ${\left(-2\right)}^{3}×{\left(-10\right)}^{3}=\left(-2\right)×\left(-2\right)×\left(-2\right)×\left(-10\right)×\left(-10\right)×\left(-10\right)=8000$
Question 8. Compare the following numbers:
(i) $2.7×{10}^{12}$;
(ii) $4×{10}^{14}$$3×{10}^{17}$
Answer: (i) $2.7×{10}^{12}$and
On comparing the exponents of base 10,
$2.7×{10}^{12}$
(ii) $4×{10}^{14}$and $3×{10}^{17}$
On comparing the exponents of base 10,
$4×{10}^{14}$