Frank Learning Maths Class 8 Chapter 2 Exponents Chapter Check-up Solutions
This post is created to help all the CBSE Class 8 students for the Solutions of Frank Learning Maths Class 8 Mathematics Book, Chapter 2 Exponents Chapter Check-up. Here students can easily find step by step solutions of all the problems for Exponents Chapter Check-up. Exercise wise proper solutions for every problems. All the problem are solved with easily understandable methods so that all the students can understand easily.
Chapter 2 – Exponents
Exponents – Chapter Check-up all Questions Solution
(1) Fill in the blanks
Solution :
(a) The reciprocal of (2/5)^-1 is – (2/5)
(b) (- 2)^2×3-1 = (- 2)^6-1 = (- 2)^5 = – 3^2
(c) (- 3/4)^5 × (5/3)^5 is equal to – 3^5/4^5 × 5^5/3^5 = (- 5/4)^5
(d) [2^-1 + 3^-1 + 4^-1]^0 = 1
(e) (6^0 – 7^0) (6^0 + 7^0) = (1 – 1) (1 + 1) = 0
(f) The standard form of 0.000064 is 6.4 × 10^-5
(g) The standard form of 234500000 is 2.345 × 10^8
(h) The usual form of 2.03 × 10^-5 is = 0.000203
(i) Cube of – 1/2 is (- 1/2)^3 = – 1/8
(j) The value of [3^-1 × 4^-1]^2 is 1/3 × 1/4 = 1/12
(2) Simplify
Solution :
(a) (1/4)-2 + (1/2)-2 + (1/3) -2
= (4) 2 + (2) 2 + (3)2
= 16 + 4 + 9
= 29…(Simplified)
(b) (-2/3) -2)3 × (1/3)-4 × 3-1 × 1/6
= ((3/2) 2) 3 × (3) 4 × 1/3 × 1/3×2
= (3 × 2/2 × 2) 3 × 32 × 32 × 1/32 × 2
= 33 × 33/23 × 23 × 32/2
= 38/28…(Simplified)
(c) 49 × z-3/7-3 × 10 × z-5 (z ≠ 0)
= 72 × z2/7-3 × 10
= 75 × z2 × 10-1…(Simplified)
(d) (25 ÷ 28) × 2-7
= 25/28 × 2-7
= 2-7/2-3
= 1/24…(Simplified)
(3) Find the value of x so that
Solution :
(a) (5/3) -2 × (5/3) -14 = (5/3) 8x
= (5/3) -16 = (5/3) 8x
= 8x = -16
= x = -2
So, the value of x will be -2
(b) (- 2) 3 × (- 2) -6 = (- 2) 2x – 1
= (- 2) -3 = (- 2) 2x – 1
= 2x -1 = -3
= 2x = -2
= x = -1
Hence, the value of x will be -1
(c) (2-1 + 4-1 + 6-1 + 8-1) x = 1
= (2-1 + 4-1 + 6-1 + 8-1) x
= (2-1 + 4-1 + 6-1 + 8-1) 0
= x = 0
Therefore, the value of x will be 0.
(4) Express each of the following in standard form
Solution :
(a) The mass of a proton in gram is 1673/1000000000000000000000000000
= 1.673 × 10-24 gram
(b) A Helium atom has a diameter of 0.000000022 cm.
= 2.2 × 10-8 cm
(c) Mass of a molecule of hydrogen gas is about 0.00000000000000000000334 tons.
= 3.34 × 10-22 tons.
(d) Human body has 1 trillion of cells which vary in shapes and sizes.
= 1 × 1012
(e) Express 56 km in m.
= 5.6 × 104 m
(f) Express 5 tons in g.
= 5 × 105 gm
(g) Express 2 years in seconds.
= 6.3072 × 107 s
(h) Express 5 hectares in cm2 (1 hectare = 10000 m2)
= 5 × 108 cm2
(5) Find the value of n
Solution :
(a) 6n/6-2 = 63
= (6) n+2 = 63
= x + 2 = 3
= x = 1
Hence, the value of n will be 1.
(b) 2n × 26/2-3 = 218
= 26+n+3 = 218
= n + 9 = 18
= n = 9
Thus, the value of n will be 9.
Question no – (6)
Solution :
As per the given question,
The diameter of the sun = 1.4 × 109 m
The diameter of the earth = 1.2756 × 107 m
∴ 1.4 × 109 m
= 1.2756 × 107 m
= 1.3 × 107 m (Approximately)
Therefore, diameter of the sun is 100 time of the Earth diameter.
Question no – (7)
Solution :
According to the question,
Mass of mars is 6.42 × 1029 kg
Mass of the sun is 1.99 × 1030 kg.
∴ 6.42 × 1029 kg + 1.99 × 1030
= 6.42 × 1029 + 19.9 × 1029
= 26.32 × 1029
= 2.632 × 1030 kg
Hence, the total mass will be 2.632 × 1030 kg.
Question no – (8)
Solution :
As per the question,
Distance between sun and earth is = 1.496 × 108 km
Distance between earth and moon is = 3.84 × 108 m
∴ Distance between moon and sun,
= – 1.496 × 108/2
= 7.48 × 107
Therefore, the distance between moon and sun will be 7.48 × 107
Question no – (11)
Solution :
According to the question,
The cells of a bacteria double itself every hour.
How many cells will there be after 8 hours,
if initially we start with 1 cell.
The answer in power will be 28
Question no – (12)
Solution :
Given, (2/9)3 × (2/9)-6 = (2/9)2x-1
= – 3 = 2x – 1
= 2x = -2
= x = -1
Therefore, the x will be -1
Question no – (13)
Solution :
Let, we should divided the number by x
∴ (- 3/2) -3/x = (4/27) -2
= -(2/3) 3 × 1/x = (27/4) 2
= – (2/3) 3 × (4/27) 2 = x
= – 23/33 × 24/36 = x
= (- 2) 7/39 = x
Therefore, (-2)7/39 should be divided.