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Mathsight Class 7 Solutions Chapter 5
Welcome to NCTB Solutions. Here with this post we are going to help 7th class students to solve MathSight Class 7 Mathematics Book, Chapter 5, Exponents and Powers. Here students can easily get all the exercise questions solution for Chapter 5, Exponents and Powers Exercise 5.1, 5.2 and 5.3
Exponents and Powers exercise 5.1 solution :
Question no – (1)
Solution :
Correct option – (a)
The exponent is 3 is not correct about 6
Question no – (2)
Solution :
Base | Exponent | ||
(a) | (-4) ⁶ | 4- | 6 |
(b) | (8/9) ² | 8/9 | 2 |
(c) | (17)⁴ | 17 | 4 |
(d) | (-2/3)⁴ | 2/3 | 4 |
(e) | (7/17)⁷ | 7/17 | 7 |
Question no – (3)
Solution :
(a) (-2)⁴
(b) -4³y²
(c) p³ q² r
(d) a²(-b)² c
(e) (-4/3)³
(f) (-3/7)³
(g) 1/5³
(h) (9/100)²
(i) (-1/10)³
Question no – (4)
Solution :
(a) a³ b² c⁵
= a × a × a × b × b × c × c × c × c × c
(b) h²y³z
= x × x × y × y × y × z
(c) p²q³
= p × p × q × q × q
(d) (3/4)²
= 3/4 × 3/4
(e) (-9) ³
=-9 × -9 × -9
Question no – (5)
Solution :
(a) 6³ = 6 × 6 × 6
= 216
(b) 12² = 12 × 12
= 144
(c) (-11/12)²
= -11/12 × -11/12
= 121/144
(d) (-3/5)³
= -3/5 × -3/5 × -3/5
= -27/125
(e) (5/-7)²
= 5/-7 × 5/-7
= 25/49
Question no – (6)
Solution :
(a) (-2)⁴ , (-3)³
= 16 > -27
(b) 7³, (6)⁴
= 343 < 1296
(c) 4² , 2⁴
= 16
= 16
(d) 10² , 5⁴
= 100 < 625
(e) 5², 2⁵
= 25 < 32
Question no – (7)
Solution :
(a) 7 + 3 × 2³
= 7 + 3 × 8
= 7 + 24
= 31
(b) 5 + 7 × (-3)²
= 5 + 7 × 9
= 5 + 63
= 68
(c) (13² – 12²)/5
= (169 -144) ÷ 5
= 25 ÷ 5
= 5
(d) 1/2 (4³ – 6 × 3²) = 1/2 (64 – 6 × 9)
= 1/2 (64 – 63)
= 1/2 × 1
= 1/2
(e) |1/4 (7 + 5²)| = |1/5 (7 + 25)|
= |1/5 × 32
= | |32/5|
(f) [ (-1/2)³ ÷ -1/4)² = -1/8 ÷ 1/16
= -1/8 × 16/1
= -2
Question no – (8)
Solution :
2500 = (50 × 50)
= (50)²
Question no – (9)
Solution :
2⁴ = 4²
∴ 4,2
Question no – (10)
Solution :
1 | 2 | 3 | 4 | 5 | |
2^{n}-1 | 1 | 3 | 7 | 15 | 31 |
2^{n}-1 | 1 | 2 | 4 | 8 | 16 |
She choose 2n-1
Question no – (11)
Solution :
2⁶ = 64
8² = 64
Exponents and Powers exercise 5.2 solution :
Question no – (1)
Solution :
(a) (-10)⁷ / (-10)²
Question no – (2)
Solution :
Correct option – (c)
write 1/4 cubed as a power is different from all.
Question no – (3)
Solution :
(a) 17-³ = 1/17³
= 1/4913
(b) 4⁷/4⁴ = 4⁷^{-11}
^{ }= 4^{-4 }= 1/4^{4}
= 1/256
(c) a⁴ × a-⁶
= a^{-24}
^{ }= 1/a^{24}
(d) (4-⁶)
= 4^{-12}
= 1/4^{12}
= 16, 777, 216
(e) (1/5-²)
= 5^{2}
= 5 × 5
= 25
Question no – (4)
Solution :
(a) y^{2} × y^{3}/y^{4} = y^{5-4}
= y = 1/y^{-1}
(b) 3/y
= (y/3)^{-1}
(c) 2/3
= (3/2)^{-1}
(d) 5^{3}/5^{4}
= 5^{-1}
(e) 1/24
= 2^{-4}
Question no – (5)
Solution :
(a) 8^{2} × 8^{3} = 8^{5}
= 20,480
(b) (-3)^{5} × (-3)^{3}
= -243 × -27
= 6,561
(c) m^{4 }× m^{7} = m^{11}
(d) (2x)^{3} × (2x)^{4}
= 8x^{3} × 16x^{4}
= 128x^{7}
(e) [(-4)^{2}]^{3}
= -4^{6}
^{ }= 4,096
(f) (3x^{0})^{3} = 3^{3}.1^{3} = 27
(g) [(-4)^{3}]^{3} = -y^{9}
(h) (2^{3}y^{3})^{-2} = 2^{6} y^{-6}
= 64y^{-6}
(i) 5^{10}÷5^{8} = 5^{10-8}
= 5^{2}
(j) (-7)^{7}÷ (-7)^{2} = 7^{9}
(k) y^{6}÷y^{12}
= y^{6-12}
^{ }= y^{-6}
(l) (4^{4})^{5}÷2^{20}
= 4^{20}/2^{20}
= (4/2)^{20}
= 2^{20}
= 104
= 8576
(m) (4/x^{2})^{3}
= 4^{3}/x^{6}
^{ }= 6^{4}/x^{6}
(n) (-y/n^{4})^{4}
= y^{4}/n^{16}
Question no – (6)
Solution :
(a) 7^{2 }×6^{2} = (4^{2})^{2}
= 1764
(b) (-4)^{3} × 5^{3} = (-20)^{3}
= -8000
(c) a^{5} ×d^{5} = a^{5}b^{5}
(d) (4y)^{2} × (3z)^{2}
= (12)^{2} y^{2}z^{2}
= 144y^{2}z^{2}
(e) 4^{2 }× 4^{4} /4
= 4 × 4^{4}
= 4^{5}
= 1024
(f) c^{8}/c^{6 }× c^{12}/c^{7}
= c^{2} × c^{5}
= c^{7}
(g) (-7)^{2 }× 3^{2}
= 49 × 9
= 441
(h) (-12)^{2} × (-4)^{3}
= 144 × (-64)
= -9216
(i) (-2)^{3} ×3^{2} × 5
= 27 × 9 × 65
= -1215
(j) 7^{2 }× 2^{2} × (-5)^{2}
= 49 × 4 × 25
= 4900
(k) 4^{2} × (-5)^{3} × 3
= 16 × (-125) × 3
= 6000
(l) 4 × 5 × 20^{2}
= 20 × 400
= 8000
Question no – (7)
Solution :
(a) 5^{0} + 7^{0} = 1+1
= 2
(b) [(-3/5)^{3}]^{2}
= -3^{6}/5^{6}
= -729/15625
(c) (6^{0}+17) ÷ 2^{5}
= (1+17) ÷ 3125
=18/3125
(d) (4^{-1 }+ 5^{-1}) ÷ 3^{2}
= (1/4 + 1/5) ÷ 9
= 5 + 4/20 × 9
= 9/20 × 9
= 1/20
(e) [(-1)^{3}]^{6 }= -1^{18}
= 1
(f) [(3/4)^{2}]^{4 }÷ [(3/4)^{4}]^{2}
= (3/4)^{8 }÷ (3/4)^{8}
= 1
Question no – (8)
Solution :
(a) (-2/5)^{8} × (-2/5)^{4} = (-2/5)^{x-1 }
Or, (-2/5)^{x-1}
= (-2/5)^{8+4}
= (-2/5)^{12}
Or, x – 1
= 12
Or, x
= 12 + 1
=13
(b) (5/9)^{12} ÷ (5/9)^{x}
= 125/729
Or, (5/9)^{12-x}
= (5/9)^{3}
Or, 12-x
= 3
Or, x
= 12 – 36
= 9
(c) (4/11)^{x }× 4/11)^{8}
= (4/11)^{15}
Or, (4/11)^{x+8}
= (4/11)^{15}
Or, x + 8
= 15
Or, x
= 15 – 8
= 7
(d) (-3/4)^{x} = (-3/4)^{8 }÷ (-3/4)^{2}
Or, (-3/4)^{x }= (-3/4)^{8-2}
= (-3/4)^{6}
Or, x = 6
Question no – (9)
Solution :
No
Exponents and Powers exercise 5.3 solution :
Question no – (1)
Solution :
(a) 3.234 × 10^{5}
= 3234 × 10^{5}/10^{3}
= 3234 × 10^{2}
= 323400
(b) 0.84 × 10^{7}
= 84 × 10^{7}/100
= 84 × 10^{7}/10^{2}
= 84 × 10^{5}
= 8400000
(c) 1.6 × 10^{-5}
= 16/10 × 10^{-5}
= 16 × 10^{-6}
= 16 × 0.000001
(d) 2.67 × 10^{-4}
= 267/10^{2} × 10^{-4}
= 267 × 10^{-2}
= 267 × 0.01
= 2.67
Question no – (2)
Solution :
(a) 44,51,00,00,000
= 4.451 × 10^{10}
(b) 0.000675
=6.75 × 10^{-4}
(c) 0. 00000083
= 8.3 × 10^{-7}
(d) 12,30,00,00,00,000
= 1. 23 × 10^{12}
Question no – (3)
Solution :
(a) 5 × 10^{8}, 9 × 10^{6}
= 500000000 > 90000000
(b) 2.4 × 10^{7}, 3.2 × 10^{8}
= 24000000 < 320000000
Question no – (4)
Solution :
= 300000
= 3 × 10^{5} km/s
Question no – (5)
Solution :
CD = 1.6 × 10^{-3}
= 0.0016
DVD = 7.4 × 10^{-4}
= 0.00074
∴ CD > DVD
Question no – (6)
Solution :
(a) heart beat about 1 min
= 60 time
∴ heart beat about 60 min
= 1 hr = 60 × 60
= 3600 time
∴ heart beat about 1 day
= 24 = 3600 × 24
= 86,400 time .
∴ Heart beat about 365 days
= 86400 × 365
= 31536000 time.
1 year blood pumps
= 31536000 × 8.3 × 10^{-2}
= 31536 × 8.3 × 10^{3} × 10^{-2}
= 261748.8 × 10
(b) 20 year blood pumps
= 261748.8 × 20 × 10
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