ICSE Class 8 Maths Selina Solutions Chapter 2 Exponents ...

ICSE Class 8 Maths Selina Solutions Chapter 2

Exponents (Powers)

Exercise 2(A) Question 1. Evaluate:

(i) (3−1 × 9−1) ÷ 3−2

Solution:

(ii) (3−1 × 4−1) ÷ 6−1

Solution:

(iii) (2−1 + 3−1)3

Solution:

(iv) (3−1 ÷ 4−1)2

Solution:

(v) (22 + 32) × (1/2)2

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Exponents (Powers)

Solution:

= (2 × 2) + (3 × 3) × (½ × ½)

= 4 + 9 × ¼ = 13/4 = 3¼ (Simplifying the given equation)

(vi) (52 − 32) × (2/3)−3

Solution:

(vii)

Solution:

(viii)

Solution:

(ix)

Solution:




Exponents (Powers)

(x) (5−1 × 3−1) + 6−1

Solution:

Question 2. 1125 = 3m × 5n; find m and n

Solution:

1125 = 32 × 53

The factors of 1125 are 3 × 3 × 5 × 5 × 5

Therefore 1125 = 3 × 3 × 5 × 5 × 5

Now comparing, 32 × 53 = 3m × 5n

Therefore m=2, n=3

Question 3. Find x, if 9 × 3x = (27)2x − 3

Solution:

9 × 3x = (27)2x − 3

32 × 3x = (3 × 3 × 3)2x − 3

(Simplifying the given equation)

⇒3x + 2 = (3)3(2x − 3)

⇒3x + 2 = (3)6x − 9

Since bases are same, compare them,

x + 2 = 6x - 9

6x – x = 9 + 2

⇒ 5x = 11

⇒ x = 11/2

(Shifting the terms)




Exponents (Powers)

Exercise 2(B)

Question 1. Compute:

(i) 18 × 30 × 53 × 22

Solution:

18 × 30 × 53 × 22

= 1 × 1 × 5 × 5 × 5 × 2 × 2

= 125 × 4 (Simplifying the given equation)

= 500

(ii) (47)2 × (4−3)4

Solution:

(47)2 × (4−3)4

= 414 × 4−12

= 414 – 12 = 42 (Simplifying the given equation)

= 4 × 4 = 16

(iii) (2−9 ÷ 2−11)3

Solution:

= (2−9 + 11)3

= (22)3 = 26

(Simplifying the given equation)

= 2 × 2 × 2 × 2 × 2 × 2 = 64

(iv)

Solution:

(v)

Solution:




Exponents (Powers)

(vi) (12)−2 ×33

Solution:

= (2 × 2 × 3)−2 × 33

= (22 × 3)−2 × 33

= 2− 2 × 2 × 3−2 × 33

=2−4 × 3−2 + 3 × 33

= 2−4 × 31

(vii) (−5)4 × (−5)6 ÷ (−5)9

Solution:

= (−5)4 + 6 − 9

= (−5)1 = −5

(viii)

Solution:

(ix) 90 × 4−1 ÷ 2−4

Solution:

= 24−2 = 22 = 4




Exponents (Powers)

(x) (625)− ¾

Solution:

(625)− ¾ = (5 × 5 × 5 × 5)– ¾

(xi)

Solution:

(xii)

Solution:

(xiii) (125)−2/3 ÷ (8)2/3

Solution:




Exponents (Powers)

(xiv) (243)2/5 ÷ (32)−2/5

Solution:

= (3 × 3 × 3 × 3 × 3)2/5 ÷ (2 × 2 × 2 × 2 × 2)−2/5

= (35)2/5 ÷ (25)−2/5

= 35×(2/5) ÷ 2(−2/5)×5 = 32 ÷ 2−2

= 32 × (1/2−2) = 32 × 2+2

= 3 × 3 × 2 × 2 = 36

(xv) (−3)4 − (∜3)0 × (−2)5 ÷ (64)2/3

Solution:

= ((−3) × (−3) × (−3) × (−3)) −1 × (−2) × (−2) × (−2) × (−2) × (−2) ÷ (26)2/3

Note: (∜3)0 = 1

= 34 + 25 ÷ 26 × (2/3)

= 34 + 25 ÷ 24 = 34 + (25/24)

= 34 + 25 – 4 = 34 + 2 = 3 × 3 × 3 × 3 + 2

= 81 + 2 = 83

(xvi)

Solution:

Question 2. Simplify:

(i)

Solution:




Exponents (Powers)

(ii) [(64)−2]−3 ÷ [{(−8)2}3]2

Solution:

= (26)−2 × −3 ÷ (−8)2 × 3 × 2

= 26 × (6) ÷ (−8)12

= 2+36 ÷ (−8)12

= 2+36 ÷ [(−2)3]12 = 236 ÷ (−2)36

= 236 – 36 = 20 = 1 (therefore a0 = 1)

(iii) (2−3 − 2−4) (2−3 + 2−4)

Solution:

= (2−3)2 − (2−4)2

{(a − b) (a + b) = a2 − b2}

Question 3. Evaluate:

(i) (−5)0

Solution:

(−5)0 = 1(a0 = 1)

(ii) 80 + 40 + 20

Solution:

80 + 40 + 20 = 1 + 1 + 1 = 3(a0 = 1)

(iii) (8 + 4 + 2)0

Solution:

(8 + 4 + 2)0 = (14)0 = 1(a0 = 1)

(iv) 4x0




Exponents (Powers)

Solution:

4x0 = 4 × 1 = 4

(v) (4x)0

Solution:

(4x)0 = 1

(vi) [(103)0]5

Solution:

[(103)0]5 = 103 × 0 × 5 = 100 = 1

(vii) (7x0)2

Solution:

(7x0)2 = 72 × x 0 × 2 = 49 × 1 = 49

(viii) 90 + 9−1 − 9−2 + 9½ − 9− ½

Solution:

Question 4. Simplify:

(i) a5b2/a2b−3

Solution:

a5b2/a2b−3 = a5−2 ⋅ b2+3 = a3b5

(ii) 15y8 ÷ 3y3

Solution:

15y8 ÷ 3y3 = 15y8/3y3

= 5y{8−3}

=5y5

(iii) x10y6 ÷ x3y−2

Solution:




Exponents (Powers)

x10y6 ÷ x3y−2 = (x10y6)/(x3y−2)

= x10−3 ⋅ y6+2

= x7y8

(iv) 5z16 ÷ 15z−11

Solution:

(v) (36x2) ½

Solution:

(36x2) ½ = (36) ½ ⋅ x2 × ½

= (6 × 6) ½ ⋅ x = (62) ½ ⋅x = 6x

(vi) (125x−3)1/3

Solution:

(125x−3)1/3 = (125)1/3x−3 × 1/3

= (5 × 5 × 5)1/3x−1

(53)1/3 ⋅ x−1 = 5x − 1

= 5/x = 5x−1

(vii) (2x2y−3)−2

Solution:

(viii) (27x−3y6)2/3

Solution:

(27x−3y6)2/3 = (27)2/3 ⋅ x−3 × (2/3) ⋅ y6 × (2/3)

= (3 × 3 × 3)2/3 x−2 ⋅ y4

= [(3 × 3 × 3)1/3]2 x−2 ⋅ y4

= 32x−2y4

= 9x−2y4

= 9y4/x2 = 9x−2y4




Exponents (Powers)

(ix) (−2x2/3y−3/2)6

Solution:

= (−2)6x(2/3) × 6 y(-3/2) × 6

= 64x4y−9

= 64x4/y9

= 64x4y−9




Exponents (Powers)



ICSE Class 8 Maths Selina Solutions Chapter 2 Exponents ...

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