NCERT Class 7 Maths Chapter 13 Exponents and Powers Exercise 13.1

Chapter 13 Exponents and Powers Exercise 13.1

Question 1: Find the value of:
(a) 2⁶
Answer:
= 2 x 2 x 2 x 2 x 2 x 2
= 64

(b) 9³
Answer:
= 9 x 9 x 9
= 729

(c) 11²
Answer:
= 11 x 11
= 121

(d) 5⁴
Answer:
= 5 x 5 x 5 x 5
= 625

Question 2: Express the following in exponential form:
(a) 6 x 6 x 6 x 6
Answer:
= 6⁴

(b) t x t
Answer:
= t²

(c) b x b x b x b
Answer:
= b⁴

(d) 5 x 5 x 7 x 7 x 7
Answer:
= 5² x 7³

(e) 2 x 2 x a x a
Answer:
= 2² x a²

(f) a x a x a x c x c x c x c x d
Answer:
= a³ x c⁴ x d¹

Question 3: Express each of the following numbers using exponential notation:
(a) 512
Answer:

(ii) 343
Answer:

(iii) 729
Answer:

(iv) 3125
Answer:

Question 4: Identify the greater number, wherever possible, in each of the following?
(i) 4³ or 3⁴
Answer:
4³ = 4 x 4 x 4
    = 64
3⁴ = 3 x 3 x 3 x 3
    = 81
64 < 81
Therefore, 3⁴ is greater.

(ii) 5³ or 3⁵
Answer:
5³ = 5 x 5 x 5
    = 125
3⁵ = 3 x 3 x 3 x 3 x 3
    = 243
125 < 243
Therefore, 3⁵ is greater.

(iii) 2⁸ or 8²
Answer:
2⁸ = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
    = 256
8² = 8 x 8
    = 64
256 < 64
Therefore, 2⁸ is greater.

(iv) 100² or 2¹⁰⁰
Answer:
100² = 100 x 100
        = 10000
2¹⁰  = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
        = 1024¹⁰
10000 < 1024¹⁰
Therefore, 2¹⁰⁰ is greater.

(v) 2¹⁰ or 10²
Answer:
2¹⁰ = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
     = 1024
10²  = 10 x 10
       = 100
1024 < 100
Therefore, 2¹⁰ is greater.

Question 5: Express each of the following as product of powers of their prime factors:
(i) 648
Answer:

(ii) 405
Answer:

(iii) 540
Answer:

(iv) 3,600
Answer:

Question 6: Simplify:
(i) 2 × 10³
Answer:
= 2 × 10 × 10 × 10
= 2 × 1000
= 2000

(ii) 7² × 2²
Answer:
= 7 × 7 × 2 × 2
= 49 × 4
= 196

(iii) 2³ × 5
Answer:
= 2 × 2 × 2 × 5
= 8 × 5
= 40

(iv) 3 × 4⁴
Answer:
= 3 × 4 × 4 × 4 × 4
= 3 × 256
= 768

(v) 0 × 10²
Answer:
= 0 × 10 × 10
= 0 × 100
= 0

(vi) 5² × 3³
Answer:
= 5 × 5 × 3 × 3 × 3
= 25 × 27
= 675

(vii) 2⁴ × 3²
Answer:
= 2 × 2 × 2 × 2 × 3 × 3
= 16 × 9
= 144

(viii) 3² × 10⁴
Answer:
= 3 × 3 × 10 × 10 × 10 × 10
= 9 × 10000
= 90000

Question 7: Simplify:
(i) (-4)³
Answer:
= -4 × -4 × -4
= -64

(ii) (-3) × (-2)³
Answer:
= -3 × -2 × -2 × -2
= -3 × -8
= 24

(iii) (-3)² × (-5)²
Answer:
= -3 × -3 × -5 × -5
= 9 × 25
= 225

(iv) (-2)³ × (-10)³
Answer:
= -2 × -2 × -2 × -10 × -10 × -10
= -8 × -1000
= 8000

Question 8: Compare the following numbers:
(i) 2.7 × 10¹² ; 1.5 × 10⁸
Answer:
2.7 × 10¹² ____ 1.5 × 10⁸
Comparing the exponents of base 10.
2.7 × 10¹² > 1.5 × 10⁸

(ii) 4 × 10¹⁴ ; 3 × 10¹⁷
Answer:
4 × 10¹⁴ ____ 3 × 10¹⁷
Comparing the exponents of base 10.
4 × 10¹⁴ < 3 × 10¹⁷