ICSE-VIII-Mathematics
02: Exponents (Powers) Class 8 Maths
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- #Section : A
- #1-i(3-1 × 9-1) ÷ 3-2Ans : (3-1 × 9-1) ÷ 3-2
(1/3 × 1/9) ÷ 1/3 × 1/3
= 1/27 ÷ 1/9
= 1/27 × 9/1= 1/3
- #1-ii(3-1 × 4-1) ÷ 6-1Ans : (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)3Ans : (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)2Ans : (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}-2Ans : {(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)2Ans : (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)-3Ans : (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)-3Ans : [(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]2Ans : [(- 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) ÷ 6-1Ans : (5-1 × 3-1) ÷ 6-1
= (1/5 × 1/3) ÷ 1/6
= 1/15 ÷ 1/6
= 1/15 × 6/1= 2/5
- Qstn #2If 1125 = 3m × 5n; find m and n.Ans : 1125 = 32 × 53
The factors of 1125 are 3 × 3 × 5 × 5 × 5
∴ 1125 = 3 × 3 × 5 × 5 × 5
Now comparing, 32 × 53 = 3m × 5n
∴ m = 2 , n = 3
- Qstn #3Find x, if 9 × 3x = (27)2x- 3Ans : 9 × 3x = (27)2x - 3
⇒ 32 × 3x = (3 × 3 × 3)2x - 3
⇒ 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
⇒ x = 2 1/5