Exponents And Powers
Class 8th Mathematics AP Board Solution
- 4−3 Simplify and give reasons
- (−2)^7 Simplify and give reasons
- Simplify and give reasons
- (−3)−4 Simplify and give reasons
- (−2)^7 × (−2)^3 × (−2)^4 Simplify the following:
- (1/2)^4 x (1/2)^5 x (1/2)^6 Simplify the following:
- Simplify the following: 4^4 (5/4)^4
- (5^-4/5^-6) ×5^3 Simplify the following:
- (−3)^4 × 7^4 Simplify the following:
- 2^2 × 3^2/2^-2 ×3-1 Simplify
- (4−1 × 3−1) ÷ 6−1 Simplify
- (4^0 + 5−1) ×5^2 × 1/3 Simplify and give reasons
- (1/2)^-3 x (1/4)^-3 x (1/5)^-3 Simplify and give reasons
- (2−1 + 3−1 + 4−1) × 3/4 Simplify and give reasons
- 3^-2/3 ×(3^0 -3-1) Simplify and give reasons
- 1 + 2−1 + 3−1 + 4^0 Simplify and give reasons
- [(3/2)^-2]^2 Simplify and give reasons
- [(3^2 - 2^2) / 1/5]^2 Simplify and give reasons
- ((5^2)^3 × 5^4) ÷ 5^6 Simplify and give reasons
- (2/3)^3 x (2/3)^5 = (2/3)^n-2 Find the value of ‘n’ in each of the following:…
- (−3)n+1 × (−3)^5 = (−3)−4 Find the value of ‘n’ in each of the following:…
- 72n+1 ÷ 49 = 7^3 Find the value of ‘n’ in each of the following:
- Find ‘x’ if 2^-3 = 1/2^x
- Simplify [(3/4)^-2 / (4/5)^-3] x (3/5)^-2
- 9m^2 - 10n^3 If m = 3 and n = 2 find the value of
- 2m^2 n^2 If m = 3 and n = 2 find the value of
- 2m^3 + 3n^2 - 5m^2 n If m = 3 and n = 2 find the value of
- mn - nm If m = 3 and n = 2 find the value of
- Simplify and give reasons (4/7)^-1 x (7/4)^-7
- 0.000000000947 Express the following numbers in the standard form.…
- 543000000000 Express the following numbers in the standard form.
- 48300000 Express the following numbers in the standard form.
- 0.00009298 Express the following numbers in the standard form.
- 0.0000529 Express the following numbers in the standard form.
- 4.37 × 10^5 Express the following numbers in the usual form.
- 5.8 ×10^7 Express the following numbers in the usual form.
- 32.5 × 10−4 Express the following numbers in the usual form.
- 3.71529 × 10^7 Express the following numbers in the usual form.
- 3789 × 10−5 Express the following numbers in the usual form.
- 24.36 × 10−3 Express the following numbers in the usual form.
- Size of the bacteria is 0.0000004 m Express the following information in the…
- The size of red blood cells is 0.000007mm Express the following information in…
- The speed of light is 300000000 m/sec Express the following information in the…
- The distance between the moon and the earth is 384467000 m (app) Express the…
- The charge of an electron is 0.0000000000000000016 coulombs Express the…
- Thickness of a piece of paper is 0.0016 cm Express the following information in…
- The diameter of a wire on a computer chip is 0.000005 cm Express the following…
- In a pack, there are 5 books, each of thickness 20 mm and 5 paper sheets each of…
- x-3 × x-2 = x-6 Rakesh solved some problems of exponents in the following way.…
- (x^2)^3 = 3x^-1 = 1/3x root x = x^8/x^2 = x^4 Rakesh solved some problems of…
- (x^2)^3 = x^2^3 = x^6 Rakesh solved some problems of exponents in the following…
- x^-2 = root x Rakesh solved some problems of exponents in the following way. Do…
- 3x^-1 = 1/3x Rakesh solved some problems of exponents in the following way. Do…
Exercise 4.1
Question 1.Simplify and give reasons
4−3
Answer:
Given, = 
= 
= 
= 
Question 2.
Simplify and give reasons
(−2)7
Answer:
Given, = (
2)7
= -(2×2×2×2×2×2×2 )∵(-2)7=-(2)7
= 128
7= 128
Question 3.
Simplify and give reasons
Answer:
Given, =
= 
= 
=
Question 4.
Simplify and give reasons
(−3)−4
Answer:
Given, =(3)-4
= 
= 
= 
(3)-4=
Question 5.
Simplify the following:
(−2)7 × (−2)3 × (−2)4
Answer:
Given, = (−2)7 × (−2)3 × (−2)4
= (−2)7+3+4 
= (−2)14
(−2)7 × (−2)3 × (−2)4=(−2)14
Question 6.
Simplify the following:
Answer:
To Find:
We know that: am × an = a(m+n)
Therefore,
=2-15
Answer.
Question 7.
Simplify the following:
44 ×
Answer:
Given, = 44 ×
= 44
= 54
= 625
Question 8.
Simplify the following:
×53
Answer:
Given, = ×53
= 
3
=
=
= 56-1
= 55
= 625
×53 = 625.
Question 9.
Simplify the following:
(−3)4 × 74
Answer:
Given, = (−3)4 × 74
= 
= 9
92401
= 194,481
(−3)4 × 74= 194,481
Question 10.
Simplify
22× 
×3-1
Answer:
Given, =22× ×3-1
= 
( )
= 
( )
= 24 × 31
= 16 × 3
= 48
22× ×3-1 = 48.
Question 11.
Simplify
(4−1 × 3−1) ÷ 6−1
Answer:
Given, = (4−1 × 3−1) ÷ 6−1
= 
= 
= 
= 
(4−1 × 3−1) ÷ 6−1 =
Question 12.
Simplify and give reasons
(40 + 5−1) ×52 ×
Answer:
Given, =(40 + 5−1) ×52 ×
=(1+
)52
= 
52
= 252-1
= 25
= 10
(40 + 5−1) ×52 × = 10
Question 13.
Simplify and give reasons
Answer:
Given, = 
= 
= 234353
= 23(22)353
= 232653
= 23+653
= 2953
= 2953
Question 14.
Simplify and give reasons
(2−1 + 3−1 + 4−1) ×
Answer:
Given, = (2−1 + 3−1 + 4−1) ×
= (
)
= (
)
= 
= 
= 
(2−1 + 3−1 + 4−1) × =
Question 15.
Simplify and give reasons
×(30 -3-1)
Answer:
Given, = ×(30 -3-1)
= 
)
= 
= 
= 
= 
×(30 -3-1) =
Question 16.
Simplify and give reasons
1 + 2−1 + 3−1 + 40
Answer:
Given, = 1 + 2−1 + 3−1 + 40
= 1 + + 
+ 1
= 
= 
1 + 2−1 + 3−1 + 40 =
Question 17.
Simplify and give reasons
Answer:
Given, = 
= [
]2
= 
= 
= 
Question 18.
Simplify and give reasons
Answer:
Given, = 
= [(9-4)5]2
= [55]2
= [52]2
= 54
=625
= 625
Question 19.
Simplify and give reasons
((52)3 × 54) ÷ 56
Answer:
Given, = ((52)3 × 54) ÷ 56
= (5654)
= (56545-6)
= 56+4-6
= 54
= 625
((52)3 × 54) ÷ 56 = 625
Question 20.
Find the value of ‘n’ in each of the following:
Answer:
Given, 
= (
= (
= (
Comparing powers of 
, we get
n2=8
n=8+2
n=10
Question 21.
Find the value of ‘n’ in each of the following:
(−3)n+1 × (−3)5 = (−3)−4
Answer:
Given, (−3)n+1 × (−3)5 = (−3)−4
(3)n+1+5 = (−3)−4
(3)n+6 = (−3)−4
Comparing powers of (3), we get
n+6 = 4
n = 4 
6
n= 10
Question 22.
Find the value of ‘n’ in each of the following:
72n+1 ÷ 49 = 73
Answer:
Given, 72n+1 ÷ 49 = 73
72n+1
= 73
72n+1
= 73
72n+1
= 73
72n+1-2 = 73
72n– 1 = 73
By comparing powers of 7, we get
2n1 = 3
2n = 3+1
2n = 4
n = 
n = 2
Question 23.
Find ‘x’ if 
Answer:
Given,
Then, find the value of x.
= 
By comparing the powers of 2, we get
x = 3
x = 3
Question 24.
Simplify
Answer:
Given, =
= [
] 
= 
= 
= 
= 
= 
Question 25.
If m = 3 and n = 2 find the value of
9m2 – 10n3
Answer:
Given, = 9m2 – 10n3
Where, m = 3 and n = 2
= 932
1023
= (99) (108)
= 81 80
= 1
9m2 – 10n3 = 1
Question 26.
If m = 3 and n = 2 find the value of
2m2 n2
Answer:
Given, = 2m2 n2
m = 3 and n = 2
2m2 n2 = 23222
= 294
= 72
2m2 n2 = 72
Question 27.
If m = 3 and n = 2 find the value of
2m3 + 3n2 – 5m2n
Answer:
Given, = 2m3 + 3n2 – 5m2n
= 233 + 322 5322
= 54 + 12 90
= 24
2m3 + 3n2 – 5m2n = 24
Question 28.
If m = 3 and n = 2 find the value of
mn – nm
Answer:
Given, = mn – nm
= 32 23
= 9 8
= 1
mn – nm = 1
Question 29.
Simplify and give reasons
Answer:
Given, = 
= 
= 
= 
= (
)2
= ()2
Exercise 4.2
Question 1.Express the following numbers in the standard form.
0.000000000947
Answer:
Given, = 0.000000000947
= 0.000000000947
= 9.47 
= 9.47 
0.000000000947 = 9.47
Question 2.
Express the following numbers in the standard form.
543000000000
Answer:
Given, = 543000000000
= 543000000000 
= 5.43 1011
9.47 = 5.43 1011
Question 3.
Express the following numbers in the standard form.
48300000
Answer:
Given, = 48300000
= 48300000 
= 4.83 107
48300000 = 4.83 107
Question 4.
Express the following numbers in the standard form.
0.00009298
Answer:
Given, = 0.00009298
= 0.00009298
= 9.28 
= 9.28 
0.00009298 = 9.28
Question 5.
Express the following numbers in the standard form.
0.0000529
Answer:
Given, = 0.0000529
= 0.0000529 
= 5.29 
0.0000529 = 5.29
Question 6.
Express the following numbers in the usual form.
4.37 × 105
Answer:
Given, = 4.37 × 105
= 4.37 100000
= 437000
4.37 × 105 = 437000.
Question 7.
Express the following numbers in the usual form.
5.8 ×107
Answer:
Given, = 5.8 ×107
= 5.8 10000000
= 58000000
5.8 ×107 = 58000000.
Question 8.
Express the following numbers in the usual form.
32.5 × 10−4
Answer:
Given, = 32.5 × 10−4
= 32.5 
= 0.00325
32.5 × 10−4 = 0.00325
Question 9.
Express the following numbers in the usual form.
3.71529 × 107
Answer:
Given, = 3.71529 × 107
= 3.71529 10000000
= 37152900
3.71529 × 107 = 37152900
Question 10.
Express the following numbers in the usual form.
3789 × 10−5
Answer:
Given, = 3789 × 10−5
= 3789 
= 0.03789
3789 × 10−5 = 0.03789
Question 11.
Express the following numbers in the usual form.
24.36 × 10−3
Answer:
Given, = 24.36 × 10−3
= 24.36 
= 0.02436
24.36 × 10−3 = 0.02436
Question 12.
Express the following information in the standard form
Size of the bacteria is 0.0000004 m
Answer:
Given, Size of the bacteria is = 0.0000004 m
= 0.0000004
= 4
= 4
Size of the bacteria is = 4 m
Question 13.
Express the following information in the standard form
The size of red blood cells is 0.000007mm
Answer:
Given, The size of red blood cells is = 0.000007mm
= 0.000007 
= 7 
The size of red blood cells = 7 mm
Question 14.
Express the following information in the standard form
The speed of light is 300000000 m/sec
Answer:
Given, The speed of light is = 300000000 m/sec
= 300000000 
= 3.0 108
The speed of light = 3.0 108m/sec.
Question 15.
Express the following information in the standard form
The distance between the moon and the earth is 384467000 m (app)
Answer:
Given, The distance between the moon and the earth,
= 384467000
= 3.84467 
108
The distance between the moon and the earth=3.84467 108 m
Question 16.
Express the following information in the standard form
The charge of an electron is 0.0000000000000000016 coulombs
Answer:
Given, The charge of an electron = 0.0000000000000000016 coulombs.
= 0.0000000000000000016 
= 1.6 
The charge of an electron = 1.6 coulombs.
Question 17.
Express the following information in the standard form
Thickness of a piece of paper is 0.0016 cm
Answer:
Given, Thickness of a piece of paper = 0.0016 cm
= 0.0016 
= 1.6 
= 1.6 
Thickness of a piece of paper = 1.6 cm.
Question 18.
Express the following information in the standard form
The diameter of a wire on a computer chip is 0.000005 cm
Answer:
Given, diameter of a wire on a computer chip = 0.000005 cm.
= 0.000005 
= 5 
= 5
The diameter of a wire on a computer chip = 5 cm.
Question 19.
In a pack, there are 5 books, each of thickness 20 mm and 5 paper sheets each of thickness 0.016mm. What is the total thickness of the pack.
Answer:
Given, thickness of book = 20mm
Thickness of paper = 0.016mm
The total thickness of the pack is to be found.
the total thickness of the pack = (520) + (50.016)
= 100 + 0.08
= 100.08
= 1.0008 102mm
the total thickness of the pack = 1.0008 102mm
Question 20.
Rakesh solved some problems of exponents in the following way. Do you agree with the solutions? If not why? Justify your argument.
x–3 × x–2 = x–6
Answer:
Given, x–3 × x–2 = x–6
the solution is wrong, because
x–3 × x–2 = x-3-2
= x-5
x–3 × x–2
x–6
Question 21.
Rakesh solved some problems of exponents in the following way. Do you agree with the solutions? If not why? Justify your argument.
Answer:
Given, 
= 
= 
Question 22.
Rakesh solved some problems of exponents in the following way. Do you agree with the solutions? If not why? Justify your argument.
Answer:
Given, 
(x2)3 = x2x3
= x6
the solution by Rakesh is wrong.
Question 23.
Rakesh solved some problems of exponents in the following way. Do you agree with the solutions? If not why? Justify your argument.
Answer:
Given,
= 
Question 24.
Rakesh solved some problems of exponents in the following way. Do you agree with the solutions? If not why? Justify your argument.
Answer:
Given,
3
= 3
= 
3