Selina Chapter 5 Exponents (including Laws of Exponents) ICSE Solutions Class 7 Maths

Selina Concise Solutions for Chapter 5 Exponents (including Laws of Exponents) Class 7 ICSE Mathematics

Exercise 5 (A)

1. Find the value of:

(i) 6²  

(ii) 7³  

(iii) 4⁴  

(iv) 5⁵  

(v) 8³  

(vi) 7⁵  

Answer 

(i) 6²   = 6 × 6 = 36

(ii) 7³   = 7 × 7 × 7 = 343

(iii) 4⁴   = 4 × 4 × 4 × 4 = 256

(iv) 5⁵  = 5 × 5 × 5 × 5 × 5 = 3125

(v) 8³   = 8 × 8 × 8 = 512

(vi) 7⁵  = 7 × 7 × 7 × 7 × 7 =16807

2.Evaluate:

(i) 2³  ×  4²  

(ii) 2³  ×  5²  

(iii) 3³  ×  5²  

(iv) 2²  ×  3³  

(v) 3²  ×  5²  

(vi) 5³ ×  2⁴  

(vii) 3² ×  4²  

(viii) (4 × 3)³  

(ix) (5 × 4)²  

Answer

(i) 2³  ×  4²  

= 2 × 2 × 2 × 4 × 4

= 8 × 16

= 128

(ii) 2³  ×  5²  

= 2 × 2 × 2 × 5 × 5

= 8 × 25

= 200

(iii) 3³  ×  5²  

= 3 × 3 × 3 × 5 × 5

= 27 × 25

= 675

(iv) 2²  ×  3³ 

= 2 × 2 × 3 × 3 × 3

= 4 × 27

= 108

(v) 3²  ×  5² 

=3 × 3 × 5 × 5 × 5

= 9 × 125

= 1125

(vi) 5³ ×  2⁴  

= 5 × 5 × 5 × 2 × 2 × 2 × 2

= 125 × 16

= 2000

(vii) 3² ×  4²  

=3 × 3 × 4 × 4

= 9 × 16

=144

(viii) (4 × 3)³  

=4 × 4 × 4 × 3 × 3 × 3

= 64 × 27

= 1728

(ix) (5 × 4)²  

=5 × 5 × 4 × 4

= 25 × 16

= 400

3. Evaluate : 

(i) (3/4)⁴  

(ii) (-5/6)⁵  

(iii) (-3/-5)³  

Answer 

4. Evaluate : 

(i) (2/3)³  × (3/4)²  

(ii) (-3/4)³  × (2/3)⁴  

(iii) (3/5)²  × (-2/3)³  

Answer 

5. Which is greater :

(i) 2³  or 3² 

(ii) 2⁵  or 5² 

(iii) 4³  or 3⁴ 

(iv) 5⁴  or 4⁵ 

Answer 

(i) 2³  or 3² 

Since, 2³   = 2 × 2 × 2 = 8

and, 3² = 3 × 3 = 9

∵ 9 is greater than 8

⇒ 3²  > 2³ 

(ii) 2⁵  or 5² 

Since, 2⁵ = 2 × 2 × 2 × 2 × 2 = 32

and, 5² = 5 × 5 = 25

∵ 32 is greater than 25

⇒ 2⁵  > 5² 

(iii) 4³  or 3⁴ 

Since, 4³   = 4 × 4 × 4 = 64

and, 3⁴  = 3 × 3 × 3 × 3 = 81

∵ 81 is greater than 64

⇒ 3⁴   > 4³ 

(iv) 5⁴  or 4⁵ 

Since, 5⁴   = 5 × 5 × 5 × 5 = 625

and, 4⁵ = 4 × 4 × 4 × 4 × 4= 1024

∵ 1024 is greater than 625

⇒ 4⁵  >  5⁴  

6. Express each of the following in exponential form :

(i) 512

(ii) 1250

(iii) 1458

(iv) 3600

(v) 1350

(vi) 1176

Answer 

7. If a = 2 and b = 3, find the value of:

(i) (a + b)²

(ii) (b – a)³

(iii) (a × b)^a

(iv) (a × b)^b

Answer 

(i) (a + b)² 

= (2 + 3)²

= (5)²

= 5 × 5 = 25

(ii) (b – a)² 

= (3 – 2)²

= (1)³ 

= 1 × 1 × 1

= 1

(iii) (a × b)^a 

= (2 × 3)²

= (6)² 

= 6 × 6

= 36

(iv) (a × b)^b 

= (2 × 3)³

= (6)³

= 6 × 6 × 6

= 216

8. Express:

(i) 1024 as a power of 2.

(ii) 343 as a power of 7.

(iii) 729 as a power of 3.

Answer 

(i) 1024 as a power of 2.

= 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

= 2¹⁰

9. If 27 × 32 = 3^x × 2^y ; find the values of x and y. 

Answer 

27 × 32 = 3^x × 2^y 
⇒ 27 = 3^x 

⇒ 27 = 3×3×3
⇒ 3³ = 3^x 

∴ x = 3
Also, 32 = 2^y 

 
32 = 2 ×2×2×2×2
⇒ 2⁵ = 2^y 
∴ y = 5 

10. If  64 × 625 = 2^a × 5^b ; find : 
(i) the values of a and b. 
(ii) 2^b × 5^a 

Answer 

(i) the values of a and b. 
64 × 625 = 2^a × 5^b 
⇒ 64 = 2^a 

⇒ 64 = 2×2×2×2×2×2
⇒ 64 = 2⁶ 
∴ a = 6 
Also, 625 = 5^b 

625 = 5×5×5×5
⇒ 625 = 5⁴ 
∴ b = 4

(ii) 2^b × 5^a 
= 2⁴ × 5⁶  
= 2×2×2×2×5×5×5×5×5×5
= 16 × 15625

= 250000

Exercise 5 (B)

1. Fill in the blanks:

In 52 = 25, base = ......... and index = ..........

If index = 3x and base = 2y, the number = .........

Answer

(i) In 5²  = 25, base = 5 and index = 2

(ii) If index = 3x and base = 2y, the number = 2y^3x 

2. Evaluate :
(i) 2⁸ ÷ 2³
(ii) 2³ ÷ 2⁸
(iii) (2⁶)⁰
(iv) (3⁰)⁶
(v) 8³ × 8^-5 × 8⁴
(vi) 5⁴ × 5³ + 5⁵
(vii) 5⁴ ÷ 5³ × 5⁵
(viii) 4⁴ ÷ 4³ × 4⁰
(ix) (3⁵ × 4⁷ × 5⁸)⁰ 

Answer 

3. Simplify, giving solution with positive index : 
(i) 2b⁶ ∙ b³ ∙ 5b⁴
(ii) x²y³ ∙ 6x⁵y ∙ 9x³y⁴
(iii) (-a⁵) (a²)
(iv) (-y²) (-y³)
(v) (-3)² (3)³
(vi) (-4x) (-5x²)
(vii) (5a²b)(2ab²) (a³b)
(viii) x^{2a + 7} ∙ x^{2a – 8}
(ix) 3^y∙3² ∙ 3^-4
(x) 2^4a∙3^3a ∙ 2^-a
(xi) 4x²y² ÷ 9x³y³
(xii) (10²)³ (x⁸)¹²
(xiii) (a¹⁰)¹⁰ (1⁶)¹⁰
(xiv) (n²)² (-n²)²
(xv) -(3ab)² (-5a²bc⁴)²
(xvi) (-2)²  × (0)³ × (3)³
(xvii) (2a³)⁴ (4a²)²
(xviii) (4x²y³)³ ÷ (3x²y³)³ 
(xix) (1/2x)³ × (6x)²
(xx) (1/4ab²c)² ÷ (3/2a²bc²)⁴
(xxi) [(5x⁷)³ ∙ (10x²)²]/(2x⁶)⁷
(xxii) [(7p²q⁹r⁵)² (4pqr)³]/(14p⁶q¹⁰r⁴)² 2

Answer 

4. Simplify and express the solution in the positive exponent form :

(i) [(-3)³ × 2⁶ ]/(6 ×2³)

(ii) [(2³)⁵ × 5⁴]/(4³ × 5²)
(iii) [36×(-6)² ×3⁶]/(12³ × 3⁵)
(iv) -128/2187
(v) [a^-7 × b^-7 × c⁵ × d⁴]/[a³ × b^-5 × c^-3 × d⁸]
(vi) (a³b^-5)^-2

Answer 

5. Evaluate
(i) 6^-2 ÷ (4^-2 × 3^-2)
(ii) [(5/6)² × 9/4]÷[(-3²/2) × (125/216)]
(iii) 5³ × 3² + (17)⁰ × 7³
(iv) 2⁵ × 15⁰ + (-3)³ – (2/7)^-2
(v) (2²)⁰ + 2^-4 ÷ 2^-6 + (1/2)^-3
(vi) 5ⁿ ×25^n-1 ÷ (5^n-1 × 25^n-1)

Answer

6. If m = -2 and n = 2 ; find the values of :

(i) m²  + n² – 2mn
(ii) mⁿ + n^m
(iii) 6m^-3 + 4n²
(iv) 2n³ – 3m

Answer 

(i) m²  + n² – 2mn

m = -2, n = 2 
= (-2)² + (2)² - 2(-2)(2) 
= 4 + 4 -(-8)

= 8 + 8 = 16 = (2)⁴