Qstnid -B-1- Compute: (I) 18 &Times; 30 &Times; 53 &Times; 22 (Ii) (47)2 &Times; (4-3)4 (Iii) (2-9 ÷ 2-11)3 (Iv) (2/3)-4 &Times; (27/8)-2 (Ix) 90 &Times; 4-1 ÷ 2-4 (V) (56/28)0 ÷ (2/5)3 &Times; 16/25 (Vi) (12)-2 &Times; 33 (Vii) (-5)4 &Times; (-5)6 ÷ (-5)9 (Viii) (-1/3)4 ÷ (-1/3)8 &Times; (-1/3)5 (X) (625)-3/4 (Xi) (27)/64)-2/3 (Xii) (1/32)-2/5 (Xiii) (125)-2/3 ÷ (8)2/3 (Xiv) (243)2/5 ÷ (32)-2/5 (Xv) <Img Border="0" Data-original-height="29" Data-original-width="220" Height="28" Src="/etl/esadigi-best/content/system/stage/icse-viii-cmn/hwh-math-selina/c02/im03.png" Width="210"> (Xvi) (27)2/3 ÷ (81/16)-1/4 - 02: Exponents (Powers) Class 8 Maths

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ICSE-VIII-Mathematics

02: Exponents (Powers) Class 8 Maths

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Qstn# B-1 Prvs-Qstn Next-Qstn

#1
Compute: (i) 1⁸ × 3⁰ × 5³ × 2² (ii) (4⁷)² × (4^-3)⁴ (iii) (2^-9 ÷ 2^-11)³ (iv) (2/3)^-4 × (27/8)^-2 (ix) 9⁰ × 4^-1 ÷ 2^-4 (v) (56/28)⁰ ÷ (2/5)³ × 16/25 (vi) (12)^-2 × 3³ (vii) (-5)⁴ × (-5)⁶ ÷ (-5)⁹ (viii) (-1/3)⁴÷ (-1/3)⁸ × (-1/3)⁵ (x) (625)^-3/4 (xi) (27)/64)^-2/3 (xii) (1/32)^-2/5 (xiii) (125)^-2/3 ÷ (8)^2/3 (xiv) (243)^2/5 ÷ (32)^-2/5 (xv) (xvi) (27)^2/3 ÷ (81/16)^-1/4
Ans : (i) 1⁸ × 3⁰ × 5³ × 2²
= 1 × 1 × 5 × 5 × 5 × 2 × 2
= 125 × 4
= 500 (ii) (4⁷)² × (4^-3)⁴
= 4¹⁴ × 4^-12
= 4^14-12= 4²
= 4 × 4
= 16 (iii) (2^-9 ÷ 2^-11)³= (2^-9/2^-11)³
= (2^-9+11)³
= (2²)³= 2⁶
= 2 × 2 × 2 × 2 × 2 × 2
= 64 (iv) (2/3)^-4 × (27/8)^-2= (2/3)^-4 × (3³/2³)^-2
= 2^-4/3^-4 × 3^-6/2^-6
= 2^-4/2^-6 × 3^-6/3^-4
= 2^-4+6 × 1/3^-4+6
= 2²/3²
= 4/9 (ix) 9⁰ × 4^-1 ÷ 2^-4= 1 × 1/4¹ × 1/2^-4
= 1 × ¼ × 2⁴= 1 × 1/2² × 2⁴
= 2^4-2= 2²
= 4 (v) (56/28)⁰ ÷ (2/5)³ × 16/25
= 1 ÷ 2³/5³ × (2 × 2 × 2 × 2)/(5 × 5) [∵ (56/28)⁰ = 1]
= 1 × 5³/2³ × 2⁴/5²= 5^3-2 × 2^4-3
= 5¹ × 2¹= 10 (vi) (12)^-2 × 3³= (2 × 2 × 3)^-2 × 3³
= (2² × 3)^-2 × 3³
= 2^-2×2 × 3^-2 × 3³
= 2^-4 × 3^-2+3
= 2^-4 × 3¹
= 3/2⁴= 3/(2 × 2 × 2 × 2)
= 3/16 (vii) (-5)⁴ × (-5)⁶ ÷ (-5)⁹
= (5)⁴ × (-5)⁶ × 1/(-5)⁹
= (-5)^4+6-9
= (-5)^10-9
= -5 (viii) (- 1/3)⁴ ÷ (- 1/3)⁸ × (- 1/3)⁵
= (- 1/3)⁴ × 1/(- 1/3)⁸ × (- 1/3)⁵
= (- 1/3)^4+5-8
= (- 1/3)^9-8
= - 1/3 (x) (625)^-3/4= (5 × 5 × 5 × 5)^-3/4
= (5⁴)^-3/4
= 5^{4× -3/4}
= 5^-3= 1/5³
= 1/(5 × 5 × 5)
= 1/125 (xi) (27/64)^-2/3= [(3³)/(4³)]^-2/3
= (3^{3× -}^2/3)/(4^{3× -2/3})
= 3^-2/4^-2
= 4²/3²= (4 × 4)/(3 × 3)= 16/9
= 1 7/9 (xii) (1/32)^-2/5
= (1/2 × 2 × 2 × 2 × 2)^2/5
= (1/2⁵)^-2/5
= 1/(2^{5× -}^2/5)
= 1/(2^-2)
= 2²
= 4 (xiii) (125)^-2/3 ÷ (8)^2/3= (5³)^-2/3 ÷ (2³)^2/3
= 5^-2/3×3 ÷ 2^3×^2/3
= 5^-2 ÷ 2²= 1/5² × 1/2²
= 1/25 × ¼= 1/100 (xiv) (243)^2/5 ÷ (32)^-2/5
= (3 × 3 × 3 × 3 × 3)^2/5 ÷ (2 × 2 × 2 × 2 × 2)^-2/5
= (3⁵)^2/5 ÷ (2⁵)^-2/5
= 3^5×^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
= (-3 × -3 × -3 × -3)
= -1 × -2 × -2 × -2 × -2 ÷ (2⁶)^2/3
Note: (∜(3)⁰= 1
= 3⁴ + (2)⁵ ÷ 2^6×^2/3
= 3⁴ + 2⁵ ÷ 2⁴= 3⁴ + 2⁵/2⁴= 3⁴ + 2^5-4 = 3⁴ + 2= 3 × 3 × 3 × 3 + 2
= 81 + 2= 83 (xvi) (27)^2/3 ÷ (81/16)^-1/4 = (3³)^2/3 ÷ (3⁴/2⁴)^-1/4
= 3^3×^2/3 ÷ (3^{1/4 ×}⁴)/(2^{1/4 ×}⁴)= 3² ÷ 3^-1/2^-1
= 3² × 2^-1/3^-1
= 3²⁺¹ × 2^-1= 3²× 1/(2⁺¹)
= (3 × 3 × 3)/2= 27/2= 13 ½

#1-i
1⁸ × 3⁰ × 5³ × 2²
Ans : 1⁸ × 3⁰ × 5³ × 2²
= 1 × 1 × 5 × 5 × 5 × 2 × 2
= 125 × 4
= 500

#1-ii
(4⁷)² × (4^-3)⁴
Ans : (4⁷)² × (4^-3)⁴
= 4¹⁴ × 4^-12
= 4^14-12= 4²
= 4 × 4
= 16

#1-iii
(2^-9 ÷ 2^-11)³
Ans : (2^-9 ÷ 2^-11)³= (2^-9/2^-11)³
= (2^-9+11)³
= (2²)³= 2⁶
= 2 × 2 × 2 × 2 × 2 × 2
= 64

#1-iv
(2/3)^-4 × (27/8)^-2
Ans : (2/3)^-4 × (27/8)^-2= (2/3)^-4 × (3³/2³)^-2
= 2^-4/3^-4 × 3^-6/2^-6
= 2^-4/2^-6 × 3^-6/3^-4
= 2^-4+6 × 1/3^-4+6
= 2²/3²
= 4/9

#1-ix
9⁰ × 4^-1 ÷ 2^-4
Ans : 9⁰ × 4^-1 ÷ 2^-4= 1 × 1/4¹ × 1/2^-4
= 1 × ¼ × 2⁴= 1 × 1/2² × 2⁴
= 2^4-2= 2²
= 4

#1-v
(56/28)⁰ ÷ (2/5)³ × 16/25
Ans : (56/28)⁰ ÷ (2/5)³ × 16/25
= 1 ÷ 2³/5³ × (2 × 2 × 2 × 2)/(5 × 5) [∵ (56/28)⁰ = 1]
= 1 × 5³/2³ × 2⁴/5²= 5^3-2 × 2^4-3
= 5¹ × 2¹= 10

#1-vi
(12)^-2 × 3³
Ans : (12)^-2 × 3³= (2 × 2 × 3)^-2 × 3³
= (2² × 3)^-2 × 3³
= 2^-2×2 × 3^-2 × 3³
= 2^-4 × 3^-2+3
= 2^-4 × 3¹
= 3/2⁴= 3/(2 × 2 × 2 × 2)
= 3/16

#1-vii
(-5)⁴ × (-5)⁶ ÷ (-5)⁹
Ans : (-5)⁴ × (-5)⁶ ÷ (-5)⁹
= (5)⁴ × (-5)⁶ × 1/(-5)⁹
= (-5)^4+6-9
= (-5)^10-9
= -5

#1-viii
(-1/3)⁴÷ (-1/3)⁸ × (-1/3)⁵
Ans : (- 1/3)⁴ ÷ (- 1/3)⁸ × (- 1/3)⁵
= (- 1/3)⁴ × 1/(- 1/3)⁸ × (- 1/3)⁵
= (- 1/3)^4+5-8
= (- 1/3)^9-8
= - 1/3

#1-x
(625)^-3/4
Ans : (625)^-3/4= (5 × 5 × 5 × 5)^-3/4
= (5⁴)^-3/4
= 5^{4× -3/4}
= 5^-3= 1/5³
= 1/(5 × 5 × 5)
= 1/125

#1-xi
(27)/64)^-2/3
Ans : (27/64)^-2/3= [(3³)/(4³)]^-2/3
= (3^{3× -}^2/3)/(4^{3× -2/3})
= 3^-2/4^-2
= 4²/3²= (4 × 4)/(3 × 3)= 16/9
= 1 7/9

#1-xii
(1/32)^-2/5
Ans : (1/32)^-2/5
= (1/2 × 2 × 2 × 2 × 2)^2/5
= (1/2⁵)^-2/5
= 1/(2^{5× -}^2/5)
= 1/(2^-2)
= 2²
= 4

#1-xiii
(125)^-2/3 ÷ (8)^2/3
Ans : (125)^-2/3 ÷ (8)^2/3= (5³)^-2/3 ÷ (2³)^2/3
= 5^-2/3×3 ÷ 2^3×^2/3
= 5^-2 ÷ 2²= 1/5² × 1/2²
= 1/25 × ¼= 1/100

#1-xiv
(243)^2/5 ÷ (32)^-2/5
Ans : (243)^2/5 ÷ (32)^-2/5
= (3 × 3 × 3 × 3 × 3)^2/5 ÷ (2 × 2 × 2 × 2 × 2)^-2/5
= (3⁵)^2/5 ÷ (2⁵)^-2/5
= 3^5×^2/5 ÷ 2^{2/5 ×}⁵= 3² ÷ 2^-2
= 3² × 1/(2^-2)= 3² × 2⁺²
= 3 × 3 × 2 × 2
= 36