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ICSE-VIII-Mathematics

02: Exponents (Powers) Class 8 Maths

with Solutions -
Qstn# A-1-i Prvs-QstnNext-Qstn
  • #1-i
    (3-1 × 9-1) ÷ 3-2 (ii) (3-1 × 4-1) ÷ 6-1 (iii) (2-1 + 3-1)3 (iv) (3-1 ÷ 4-1)2 (ix) {(3/5)-2}-2 (v) (22 + 32) × (1/2)2 (vi) (52- 32) × (2/3)-3 (vii) [(1/4)-3- (1/3)-3] ÷ (1/6)-3 (viii) [(- ¾)-2]2 (x) (5-1× 3-1) ÷ 6-1
    Ans : (3-1 × 9-1) ÷ 3-2
    (1/3 × 1/9) ÷ 1/3 × 1/3
    = 1/27 ÷ 1/9
    = 1/27 × 9/1= 1/3 (ii) (3-1× 4-1) ÷ 6-1
    = (1/3 × 1/4) ÷ 1/6
    = 1/12 ÷ 1/6
    = 1/12 × 6/1= ½ (iii) (2-1 + 3-1)3
    = (1/2 + 1/3)3= {(1 × 3)/(2 × 3) + (1 × 2)/(3 × 2)}3
    = {(3 + 2)3/6}
    = (5/6)3
    = (5 × 5 × 5)/(6 × 6 × 6)
    = 125/216 (iv) (3-1 ÷ 4-1)2
    = (1/3 ÷ ¼)2
    = (1/3 × 4/1)2= (4/3)2
    = 16/9= 1 7/9 (ix) {(3/5)-2}-2= (3/5)-2×(-2)= (3/5)4
    = (3 × 3 × 3 × 3)/(5 × 5 × 5 × 5)
    = 81/625 (v) (22 + 32) × (1/2)2
    = (2 × 2) + (3 × 3) × (1/2 × 1/2)
    = 4 + 9 × 1/4= 13/4= 3 1/4 (vi) (52 - 32) × (2/3)-3
    = (5 × 5) - (3 × 3) × (3/2)3
    = 25 - 9 × (3/2 × 3/2 × 3/2)
    = 16 × 27/8= 54 (vii) [(1/4)-3 - (1/3)-3] ÷ (1/6)-3
    = [(4/1)3 - (3/1)3] ÷ (6/1)3
    = (4/1 × 4/1 × 4/1 - 3/1 × 3/1 × 3/1) ÷ (6/1)3
    = 64 - 27 × (1/6 × 1/6 × 1/6)
    = 37 × 1/216= 37/216 (viii) [(- ¾)-2]2= (- ¾)-2×2= (- ¾)-4
    = (4/3)4= (4 × 4 × 4 × 4/3 × 3 × 3 × 3)
    = 256/81
    = 3 13/81 (x) (5-1 × 3-1) ÷ 6-1
    = (1/5 × 1/3) ÷ 1/6
    = 1/15 ÷ 1/6
    = 1/15 × 6/1= 2/5
  • #1-ii
    (3-1 × 4-1) ÷ 6-1
    Ans : (3-1× 4-1) ÷ 6-1
    = (1/3 × 1/4) ÷ 1/6
    = 1/12 ÷ 1/6
    = 1/12 × 6/1= ½
  • #1-iii
    (2-1 + 3-1)3
    Ans : (2-1 + 3-1)3
    = (1/2 + 1/3)3= {(1 × 3)/(2 × 3) + (1 × 2)/(3 × 2)}3
    = {(3 + 2)3/6}
    = (5/6)3
    = (5 × 5 × 5)/(6 × 6 × 6)
    = 125/216
  • #1-iv
    (3-1 ÷ 4-1)2
    Ans : (3-1 ÷ 4-1)2
    = (1/3 ÷ ¼)2
    = (1/3 × 4/1)2= (4/3)2
    = 16/9= 1 7/9
  • #1-ix
    {(3/5)-2}-2
    Ans : {(3/5)-2}-2= (3/5)-2×(-2)= (3/5)4
    = (3 × 3 × 3 × 3)/(5 × 5 × 5 × 5)
    = 81/625
  • #1-v
    (22 + 32) × (1/2)2
    Ans : (22 + 32) × (1/2)2
    = (2 × 2) + (3 × 3) × (1/2 × 1/2)
    = 4 + 9 × 1/4= 13/4= 3 1/4
  • #1-vi
    (52- 32) × (2/3)-3
    Ans : (52 - 32) × (2/3)-3
    = (5 × 5) - (3 × 3) × (3/2)3
    = 25 - 9 × (3/2 × 3/2 × 3/2)
    = 16 × 27/8= 54
  • #1-vii
    [(1/4)-3- (1/3)-3] ÷ (1/6)-3
    Ans : [(1/4)-3 - (1/3)-3] ÷ (1/6)-3
    = [(4/1)3 - (3/1)3] ÷ (6/1)3
    = (4/1 × 4/1 × 4/1 - 3/1 × 3/1 × 3/1) ÷ (6/1)3
    = 64 - 27 × (1/6 × 1/6 × 1/6)
    = 37 × 1/216= 37/216
  • #1-viii
    [(- ¾)-2]2
    Ans : [(- ¾)-2]2= (- ¾)-2×2= (- ¾)-4
    = (4/3)4= (4 × 4 × 4 × 4/3 × 3 × 3 × 3)
    = 256/81
    = 3 13/81
  • #1-x
    (5-1× 3-1) ÷ 6-1
    Ans : (5-1 × 3-1) ÷ 6-1
    = (1/5 × 1/3) ÷ 1/6
    = 1/15 ÷ 1/6
    = 1/15 × 6/1= 2/5