icse class 8 maths selina solutions chapter 2 exponents
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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
ICSE Class 8 Maths Selina Solutions Chapter 2
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:
ICSE Class 8 Maths Selina Solutions Chapter 2
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)
ICSE Class 8 Maths Selina Solutions Chapter 2
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:
ICSE Class 8 Maths Selina Solutions Chapter 2
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
ICSE Class 8 Maths Selina Solutions Chapter 2
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:
ICSE Class 8 Maths Selina Solutions Chapter 2
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:
ICSE Class 8 Maths Selina Solutions Chapter 2
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
ICSE Class 8 Maths Selina Solutions Chapter 2
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:
ICSE Class 8 Maths Selina Solutions Chapter 2
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
ICSE Class 8 Maths Selina Solutions Chapter 2
Exponents (Powers)
(ix) (−2x2/3y−3/2)6
Solution:
= (−2)6x(2/3) × 6 y(-3/2) × 6
= 64x4y−9
= 64x4/y9
= 64x4y−9
ICSE Class 8 Maths Selina Solutions Chapter 2
Exponents (Powers)
ICSE Class 8 Maths Selina Solutions Chapter 2
Exponents (Powers)
ICSE Class 8 Maths Selina Solutions Chapter 2
Exponents (Powers)
ICSE Class 8 Maths Selina Solutions Chapter 2
Exponents (Powers)
ICSE Class 8 Maths Selina Solutions Chapter 2
Exponents (Powers)
ICSE Class 8 Maths Selina Solutions Chapter 2
Exponents (Powers)