AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions

SCERT AP 7th Class Maths Solutions Pdf Chapter 78 Exponents and Powers InText Questions and Answers.

AP State Syllabus 7th Class Maths Solutions 8th Lesson Exponents and Powers InText Questions

Check Your Progress [Page No. 28]

Question 1.
Write the following in exponential form by using 10 as the base number :
(i) 10,00,00,000
(ii) 100,00,00,000
Answer:

NumberExpanded formExponential
(i) 10,00,00,00010 × 10 × 10 × 10 × 10 × 10 × 10 × 10108
(ii) 100,00,00,00010 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10109

Let’s Explore [Page No. 29]

Question 1.
Observe and complete the following table. First one is done for you.
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 1
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 2

Question 2.
Write the following numbers in exponential form. Also state the base, exponent and how to read. .
(i) 16
(ii) 49
(iii) 512
(iv) 243
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 3

Question 3.
Compute the following and write the greater one.
(i) 43 or 34
Answer:
43 = 4 × 4 × 4 = 64
34 = 3 × 3 × 3 × 3 = 81 is greater.
64 < 81 (or) 81 > 64
So, 43 < 34 (or) 34 > 43

(ii) 53 or 35
Answer:
53 = 5 × 5 × 5 = 125
35 = 3 × 3 × 3 × 3 × 3 = 243 is greater.
125 < 243 (or) 243 > 125
So, 53 < 35 (or) 35 > 53

AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions

Question 4.
Is 32 equal to 23 ? Justify your answer.
Answer:
32 = 3 × 3 = 9
23 = 2 × 2 × 2 = 8
9 ≠ 8
32 ≠ 23
So, ab ≠ ba unless a = b

Check Your Progress [Page No. 30]

Express the following number in exponential form using prime factorisation:
(i) 432
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 4
432 = 2 × 216
= 2 × 2 × 108
= 2 × 2 × 2 × 54
= 2 × 2 × 2 × 2 × 27
= 2 × 2 × 2 × 2 × 3 × 9
= 2 × 2 × 2 × 2 × 3 × 3 × 3
∴ 432 = 24 × 33

(ii) 1296
Answer:
1296 = 2 × 648
= 2 × 2 × 324
= 2 × 2 × 2 × 162
= 2 × 2 × 2 × 2 × 81
= 2 × 2 × 2 × 2 × 3 × 27
= 2 × 2 × 2 × 2 × 3 × 3 × 9
= 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 5
∴ 1296 = 24 × 34

(iii) 729
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 6
729 = 3 × 243
= 3 × 3 × 81
= 3 × 3 × 3 × 27
= 3 × 3 × 3 × 3 × 9
= 3 × 3 × 3 × 3 × 3 × 3
729 = 36

(iv) 1600
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 7
1600 = 2 × 800
= 2 × 2 × 400
= 2 × 2 × 2 × 200
= 2 × 2 × 2 × 2 × 100
= 2 × 2 × 2 × 2 × 2 × 50
= 2 × 2 × 2 × 2 × 2 × 2 × 25
= 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5
1600 = 26 × 52

Let’s Explore [Page No. 32]

Question 1.
Write the appropriate number in place of ▢ in the following.
Let ‘b’ be any non-zero integer.
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 8
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 9
= b2 × b3
= b × b × b × b × b = b5
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 10

AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 11
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 12
then b10 × b1 = b14
b10+1 = b14
b11 ≠ b14
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 13
then b10 × b2 = b14
b10+2 = b14
b12 ≠ b14
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 14
then b10 × b3 = b14
b10+3 = b14
b13 ≠ b14
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 15
then b10 × b4 = b14
b10+4 = b14
∴ b14 = b14
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 16

AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions

Question 2.
Simplify the following using the formula am × an = am+n
(i) 57 × 54
Answer:
57 × 54
We know that am × an = am+n;
57 × 54 = 57+4 = 511
∴ 57 × 54 = 511

(ii) p3 × p2
Answer:
p3 × p2
We know that am × an = am+n
p3 × p2 = p3+2 = p5
∴ p3 × p2 = p5

(iii) (-4)10 × (-4)3 × (-4)2
Answer:
(-4)10 × (-4)3 × (-4)2
We know that am × an = am+n
(- 4)10+3+2 = (- 4)15
∴ (-4)10 × (-4)3 × (-4)2 = (- 4)15

Let’s Explore [Page No. 33]

Question 1.
Write the following in exponential form using the formula (am)n = amn.
(i) (62)4
Answer:
(62)4
We know (am)n = amn
(62)4 = 62×4 = 68
∴ (62)4 = 68

(ii) (22)100
Answer:
(22)100
We know (am)n = amn
(22)100 = 22×100 = 2200
∴ (22)100 = 2200

(iii) (206)2
Answer:
(206)2
We know (am)n = amn
(206)2 = 206×2 = 2012
∴ (206)2 = 2012

(iv) [(-10)3]5
Answer:
[(-10)3]5
We know (am)n = amn
[(-10)3]5 =(-10)3×5 = (-10)15
∴ [(- 10)3]5 = (- 10)15

AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions

Check Your Progress [Page No. 34]

Simplify the following by using the law , am × bm = (ab)m.
(i) 76 × 36
Answer:
76 × 36
We know, am × bm = (ab)m
76 × 36 = (7 × 3)6 = (21)6
∴ 76 × 36 = 216

(ii) (3 × 5)4
Answer:
(3 × 5)4
We know, (ab)m = am × bm
(3 × 5)4 = 34 × 54
∴ (3 × 5)4 = 34 × 54

(iii) a4 × b4
Answer:
a4 × b4
We know, am × bm = (ab)m
a4 × b4 = (a . b)4
∴ a4 × b4 = (a . b)4

(iv) 32 × a2
Answer:
32 × a2
We know, am × bm = (ab)m
32 × a2 = (3 × a)2 = (3a)2
∴ 32 × a2 = (3a)2

Let’s Explore [Page No. 37]

Question 1.
Simplify and write In the form of am-n Or \(\frac{1}{\mathbf{a}^{\mathbf{n}-\mathbf{m}}}\)
(i) \(\frac{10^{8}}{10^{4}}\)
Answer:
We Know \(\frac{10^{8}}{10^{4}}\) = am-n
\(\frac{10^{8}}{10^{4}}\) = 108-4 = 104
∴\(\frac{10^{8}}{10^{4}}\) = 104

(ii) \(\frac{(-7)^{13}}{(-7)^{10}}\)
Answer:
\(\frac{(-7)^{13}}{(-7)^{10}}\)
We Know \(\frac{a^{m}}{a^{n}}\) = am-n (m > n)
\(\frac{(-7)^{13}}{(-7)^{10}}\) = (-7)13-10
= (-7)3 = -7 × -7 × -7 = – 343
∴\(\frac{(-7)^{13}}{(-7)^{10}}\) = – 343

(iii) \(\frac{12^{5}}{12^{8}}\)
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 17

(iv) \(\frac{3^{4}}{3^{7}}\)
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 18

AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions

Question 2.
Fill the appropriate number In the box
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 19
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 20
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 21
We Know \(\frac{a^{m}}{a^{n}}\) = am-n (m > n)
\(\frac{7^{12}}{7^{7}}\) = 712-7 = 75
∴ \(\frac{7^{12}}{7^{7}}\) = 75
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 22

AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 23
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 24

AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 25
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 26

AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 27
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 28

Question 3.
Simplify the following :
(i) \(\frac{6^{8}}{6^{8}}\)
Answer:
\(\frac{6^{8}}{6^{8}}\)
We Know \(\frac{a^{m}}{a^{n}}\) = am-n
\(\frac{6^{8}}{6^{8}}\) = 68-8 = 60 = 1 (∵ a0 = 1)

(ii) \(\frac{t^{10}}{t^{10}}\)
Answer:
\(\frac{t^{10}}{t^{10}}\)
We Know \(\frac{a^{m}}{a^{n}}\) = am-n
\(\frac{t^{10}}{t^{10}}\) = t10-10 = t0 = 1 (∵ a0 = 1)

(iii) \(\frac{12^{7}}{12^{7}}\)
Answer:
\(\frac{12^{7}}{12^{7}}\)
We Know \(\frac{a^{m}}{a^{n}}\) = am-n
\(\frac{12^{7}}{12^{7}}\) = 127-7 = 120 = 1 (∵ a0 = 1)

(iv) \(\frac{p^{5}}{p^{5}}\)
Answer:
\(\frac{p^{5}}{p^{5}}\)
We Know \(\frac{a^{m}}{a^{n}}\) = am-n
\(\frac{p^{5}}{p^{5}}\) = p10-10 = p0 = 1 (∵ a0 = 1)

Check Your Progress [Page No. 38]

Question 1.
Complete the following boxes .
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 29
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 30

AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 31
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 32

AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 33
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 34

AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 35
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 36

Check Your Progress [Page No. 39]

Question 1.
Express the following in exponential form.
(i) \(\frac{-27}{125}\)
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 37

(ii) \(\frac{-32}{243}\)
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 38

(iii) \(\frac{-125}{1000}\)
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 39

(iv) \(\frac{-1}{625}\)
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 40

AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions

Let’s Think [Page No. 39]

Question 1.
Deekshltha and Harsha computed 4(3)2 in different ways.
Deeksbitha did it like this
4(3)2 = (4 × 3)2
= 122
= 144

Harsha did it like this
4(3)2 = 4 × (3 × 3)
= 4 × 9
= 36
Who has done the problem Incorrectly?
Discuss the reason for the mistake with your friends.
Answer:
In 4(3)2 square only belongs to 3, but not 4.
So, Deekshitha did wrong and Harsha did correct.

Let’s Do Activity [Page No. 40]

Finding the pair : Divide the classroom into two groups. Each group has a set of cards. Each student of group 1 has to pair with one suitable student of group 2 by stating in the reason.
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 41
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 42
Note : This activity can be extended till all the children in the class are familiarised with the laws of exponents.

Project Work [Page No. 42]

Collect the annual income of 5 families in your location by observing their ration card and rounded into the nearest thousand / Lakh and express in the exponential form. One done for you.
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 43
Answer:
AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions 44

Examples:

Question 1.
Which one is greater 82 or 28? Justify.
Answer:
82 = 8 × 8 = 64
28 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 256
256 >64
Therefore, 28 > 82.

Question 2.
Simplify the following using the formula am × an = am+n
(i) (- 5)7 × (- 5)4
Answer:
(- 5)7 × (- 5)4 = (- 5)7+4
(∵ am × an = am+n)
= (- 5)11
∴ (- 5)7 × (- 5)4 = (- 5)11

(ii) 33 × 32 × 34
Answer:
33 × 32 × 34 = 33+2+4
(∵ am × an = am+n)
= 39
∴ 33 × 32 × 34 = 39

AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions

Question 3.
Simplify the following using the formula (am)n = amn
(i) (83)4
Answer:
(83)4 = 83×4
= 812
∴ (83)4 = 812

(ii) [(-11)5]2
Answer:
[(-11)5]2 = (- 11)5×2
= (- 11)10
∴ [(-11)5]2 = (- 11)10

(iii) (750)2
Answer:
(750)2= 750×2 = 7100
∴ (750)2 = 7100

Question 4.
Simplify the following using the expo-nential law am × bm = (ab)m
(i) 52 × 32
Answer:
52 × 32 = (5 × 3)2 [∵ am × bm = (ab)m]

(ii) p3 × q3
Answer:
p3 × q3 = (p × q)3

(iii) (7 × 8)4
Answer:
(7 × 8)4 = 74 × 84 [∵ (ab)m = am × bm]

Question 5.
Simplify the following and write in the form of \(\frac{a^{m}}{a^{n}}\) = am-n or \(\frac{a^{m}}{a^{n}}=\frac{1}{a^{n-m}}\)
(i) \(\frac{2^{9}}{2^{3}}\)
Answer:
\(\frac{2^{9}}{2^{3}}\) = 29-3 [∵ \(\frac{a^{m}}{a^{n}}\) = am-n]
= 26

(ii) \(\frac{(-9)^{11}}{(-9)^{7}}\)
Answer:
\(\frac{(-9)^{11}}{(-9)^{7}}\) = (- 9)11-7 = (-9)4

(iii) \(\frac{7^{10}}{7^{13}}\)
Answer:
\(\frac{7^{10}}{7^{13}}=\frac{1}{7^{13-10}}\)
[∵ \(\frac{a^{m}}{a^{n}}=\frac{1}{a^{n-m}}\)]
= \(\frac{1}{7^{3}}\)

(iv) \(\frac{6^{2}}{6^{5}}\)
Answer:
\(\frac{6^{2}}{6^{5}}=\frac{1}{6^{5-2}}=\frac{1}{6^{3}}\)

Question 6.
Simplify the following by using formula \(\frac{a^{m}}{b^{m}}=\left(\frac{a}{b}\right)^{m}\).
(i) \(\frac{5^{3}}{2^{3}}\)
Answer:
\(\frac{5^{3}}{2^{3}}=\left(\frac{5}{2}\right)^{3}\) [∵ \(\frac{a^{m}}{b^{m}}=\left(\frac{a}{b}\right)^{m}\)]

(ii) \(\left(\frac{8}{5}\right)^{4}\)
Answer:
\(\left(\frac{8}{5}\right)^{4}=\frac{8^{4}}{5^{4}}\)
[∵ \(\frac{a^{m}}{b^{m}}=\left(\frac{a}{b}\right)^{m}\)]

Question 7.
Evaluate:
(1)4, (1)5, (1)7, (- 1)2, (- 1)3, (- 1)4, (- 1)5
Answer:
(1)4 = 1 × 1 × 1 × 1 = 1
(1)5 = 1 × 1 × 1 × 1 × 1 = 1
(1)7 = 1 × 1 × 1 × 1 × 1 × 1 × 1 = 1
(- 1)2= (-1) × (-1) = 1
(- 1)3 = (-1) × (1) × (-1) = – 1
(- 1)4 =(-1) × (-1) × (-1) × (-1) = 1
(- 1)5 = (-1) × (-1) × (-1) × (-1) × (- 1) = – 1

From the above illustrations,
(i) It raised. to any power is 1.
(ii) (-1) raised to even power is (- 1) and
(-1) raised to an odd power is (-1).

Thus (- 1)m = 1 if ’m’ is even
(- 1)m 1 if ‘m’ is odd

Question 8.
Express \(\) In exponential form.
Answer:
-8 = (-2) × (-2) × (-2) = (-2)3
27 = 3 × 3 × 3 = (3)3
∴ \(\frac{-8}{27}: \frac{(-2)^{3}}{3^{3}}=\left(\frac{-2}{3}\right)^{3}\)

Question 9.
Abhllash computed a3. a2 as a6. Is it correct?
Answer:
Abhilash has done it incorrectly.
Bcause a3. a2 = a3+2 = a5 [∵ am . an = amn]
Therefore, a3. a2 = a5 is correct answer.

Question 10.
Riyaz computed \(\frac{a^{8}}{a^{2}}\) as a4. Has he done It correctly? Justify your answer.
Answer:
Riyaz has done it incorrectly.
Because \(\frac{a^{8}}{a^{2}}\) = a8-2
= a6 [∵ \(\frac{a^{m}}{a^{n}}\) = am-n]
∴ \(\frac{a^{8}}{a^{2}}\) = a6 is correct answer.

AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions

Question 11.
Write the following into standard form.
(i) 7465
Answer:
7465 = 7.465 × 1000 (Decimal is shifted three places to the left)
= 7.465 × 103

(ii) The height of Mount Everest is 8848 m.
Answer:
The height of Mount Everest
= 8848 m
= 8.848 × 1000 m (Decimal is shifted three places to the left)
= 8.848 × 103m

(iii) The distance from the Sun to Earth is 149,600,000,000 m.
Answer:
The distance from the Sun to Earth
= 149,600,000,000 m
= 1.496 × 100000000000 m
= 1.496 × 1011 m

Reasoning Corner [Page No. 45: Odd one out in numbers]

In each of the following questions, there are 4 numbers. Three of them are similar in a certain way but one is not like the other three. One has to identify the similarity and then strike the odd one out as answer option.
The number can be odd/ even /consecutive, prime numbers, multiple of some number, single, square or cubes of different numbers, plus/minus of some other number or combinations of any mathematical calculation.
Question 1.
(a) 12
(b) 25
(c) 37
(d) 49
Answer:
(c) 37

Hint:
Prime number

Question 2.
(a) 13
(b) 63
(c) 83
(d) 43
Answer:
(b) 63

Hint:
Not a prime number

Question 3.
(a) 21
(b) 49
(c) 56
(d) 36
Answer:
(d) 36

Hint:
Not divisible by 7

Question 4.
(a) 112
(b) 256
(c) 118
(d) 214
Answer:
(b) 256

Hint:
Square number

AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions

Question 5.
(a) 42
(b) 21
(c) 84
(d) 35
Answer:
(d) 35

Hint:
Not divisible by 3

Question 6.
(a) 11
(b) 13
(c) 15
(d) 17
Answer:
(c) 15

Hint:
Not a prime number

Question 7.
(a) 10
(b) 11
(c) 15
(d) 16
Answer:
(b) 11

Hint:
Prime number

Question 8.
(a) 49
(b) 63
(c) 77
(d) 81
Answer:
(d) 81

Hint:
Not divisible by 7

Question 9.
(a) 28
(b) 65
(c) 129
(d) 215
Answer:
(a) 28

Hint:
Even number

Question 10.
(a) 51
(b) 144
(c) 64
(d) 121
Answer:
(a) 51

Hint:
Not square number

Practice Questions [Page No. 46]

Question 1.
(a) 3
(b) 9
(c) 5
(d) 7
Answer:
(b) 9

Explanation:
9 is composite number. The remaining numbers are primes.

AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions

Question 2.
(a) 6450
(b) 1776
(c) 2392
(d) 3815
Answer:
(d) 3815

Explanation:
All others are even numbers.

Question 3.
(a) 24
(b) 48
(c) 42
(d) 12
Answer:
(c) 42

Explanation:
12, 24 and 48 are multiples of 12.

Question 4.
(a) 616
(b) 252
(c) 311
(d) 707
Answer:
(c) 311

Explanation:
616, 252 and 707 are Palindromes.

Question 5.
(a) 18
(b) 12
(c) 30
(d) 20
Answer:
(d) 20

Explanation:
12, 18 and 30 are 3 (or) 6 multiples. But, 20 is not 3 (or) 6 multiple.

Question 6.
Find the odd one from the given
(a) 3730
(b) 6820
(c) 5568
(d) 4604
Answer:
(a) 3730

Explanation:
3730, All others are divisible by 4.

Question 7.
(a) 2587
(b) 7628
(c) 8726
(d) 2867
Answer:
(a) 2587

Explanation:
All others are formed by 2, 6, 7 and 8.

Question 8.
(a) 63
(b) 29
(c) 27
(d) 25
Answer:
(d) 25

Explanation:
63, 29 and 27 are not squares. 25 only the square.

AP Board 7th Class Maths Solutions Chapter 8 Exponents and Powers InText Questions

Question 9.
(a) 23
(b) 37
(c) 21
(d) 31
Answer:
(c) 21

Explanation:
23,37 and 31 are prime numbers.
21 only the composite number.

Question 10.
(a) 18
(b) 9
(c) 21
(d) 7
Answer:
(d) 7

Explanation:
18, 9, 21 are composite numbers.
7 only the prime number.