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Class 8th Mathematics RS Aggarwal Solution
Exercise 2a
  1. Evaluate:(i) 4-3(ii) (1/2)^-5 (iii) (4/3)^-3 (iv) (-3)-4(v) (-2/3)^-5…
  2. (i) (5/3)^2 x (5/3)^2 (ii) (5/6)^6 x (5/6)^-4 (iii) (2/3)^-3 x (2/3)^-2 (iv)…
  3. (i) (5/9)^-2 x (3/5)^-3 x (3/5)^0 (ii) (-3/5)^-4 x (-2/5)^2 (iii) (-2/3)^-3 x…
  4. (i) (-2/3)^2^-2 (ii) [(-1/3)^2^-2]^-1 (iii) (3/2)^-2^2 Evaluate:
  5. Evaluate (1/3)^-3 - (1/2)^-3 / (1/4)^-3
  6. Evaluate (4/3)^-1 - (1/4)^-1^-1
  7. Evaluate [(5-1 3-1)-1 6-1]
  8. Find the value of: (i) (20+ 3-1) 3^2 (ii) (2-1 3-1) 2-3 (iii) (1/2)^-2 +…
  9. (5/3)^-4 x (5/3)^-5 = (5/3)^3x Find the value of x for which
  10. (4/9)^4 x (4/9)^-7 = (4/9)^2x-1 Find the value of x for which
  11. By what number should (-6)-1 be multiplied so that the product becomes 9-1?…
  12. By what number should (-2/3)^-3 be divided so that the quotient may be…
  13. If 5^2x+1 / 25 = 125 , find the value of x.
Exercise 2b
  1. (i) 57.36 (ii) 3500000 (iii) 273000 (iv) 168000000 (v) 4630000000000 (vi) 345…
  2. (i) 3.74 10^5 (ii) 6.912 10^8 (iii) 4.1253 10^7 (iv) 2.5 10^4 (v) 5.17 10^8 (vi)…
  3. The height of Mount Everest is 8848 m. Write it in standard form.…
  4. The speed of light is 300000000 m/sec. express it in standard form.…
  5. The distance from the earth to the sun is 149600000000 m. Write it in standard…
  6. Mass of earth is (5.97 x 10^24) kg and mass of moon is (7.35 x 10^22) kg. What…
  7. (i) 0.0006 (ii) 0.00000083 (iii) 0.0000000534 (iv) 0.0027 (v) 0.00000165 (vi)…
  8. 1 micron = 1/1000000 m. Express it in standard form.
  9. Size of a bacteria = 0.0000004 m. Express it in standard form.
  10. Thickness of a paper = 0.03 mm. Express it in standard form.
  11. (i) 2.06x10-5 (ii) 5 x10-7 (iii) 6.82 x 10-6 (iv) 5.673x10-4 (v) 1.8 x10-2 (vi)…
Exercise 2c
  1. The value of (2/5)^-3 isA. - 8/125 B. 25/4 C. 125/8 D. - 2/5
  2. The value of (-3)^-4 isA. 12 B. 81 C. - 1/12 D. 1/81
  3. The value of (-2)^-5 isA. -32 B. -1/32 C. 32 D. 1/32
  4. The value of (2-5 2-2) isA. 1/128 B. -1/128 C. - 1/8 D. 1/8
  5. The value of (3^-1 + 4^-1) / 5^-1 isA. 7/10 B. 60/7 C. 7/5 D. 7/15…
  6. (1/2)^-2 + (1/3)^-2 + (1/4)^-2 = ? Choose the correct answer:A. 61/144 B. 144/61…
  7. (1/3)^-3 - (1/2)^-3 / (1/4)^-3 = ? Choose the correct answer:A. 19/64 B. 27/16…
  8. [(-1/3)^2^-2]^-1 =? Choose the correct answer:A. 1/16 B. 16 C. - 1/16 D. -16…
  9. The value of x for which (7/12)^-4 x (7/12)^3x = (7/12)^5 isA. -1 B. 1 C. 2 D. 3…
  10. If (2^3x+1 + 10) / 7 = 6 , then x is equal toA. -2 B. 0 C. 1 D. 2…
  11. (2/3)^0 = ? Choose the correct answer:A. 3/2 B. 2/3 C. 1 D. 0
  12. (-5/3)^-1 = ? Choose the correct answer:A. 5/3 B. 3/5 C. -3/5 D. None of these…
  13. (- 1/2)^3 = ? Choose the correct answer:A. -1/6 B. 1/6 C. 1/8 D. -1/8…
  14. (- 3/4)^2 = ? Choose the correct answer:A. -9/16 B. 9/16 C. 16/9 D. -16/9…
  15. 3670000 in standard form isA. 367 10^4 B. 36.7 10^5 C. 3.67 10^6 D. None of…
  16. 0.0000463 in standard form isA. 463 10-7 B. 4.63 10-5 C. 4.63 10-9 D. 46.3 10-6…
  17. 0.000367 10^4 in usual form isA. 3.67 B. 36.7 C. 0.367 D. 0.0367
Cce Test Paper-2
  1. Evaluate (i) 3-4 (ii) (-4)^3 (iii) (3/4)^-2 (iv) (5/7)^0
  2. Evaluate: (-2/3)^3^-2
  3. Simplify: (3^-1 + 6^-1) / (3/4)^-1
  4. By what number should (-2/3)^-3 be divided so that the quotient is (4/9)^-2 ?…
  5. By what number should (-3)^-1 be multiplied so that the quotient is 6^-1 ?…
  6. Express each of the following in standard form: (i) 345 (ii) 180000 (iii) 0.000003 (iv)…
  7. The value of (-3)^-3 isA. -27 B. 9 C. -1/27 D. 1/27
  8. The value of (3/4)^-3 isA. -27/64 B. 64/27 C. -9/4 D. 27/64
  9. Choose the corret answer: (3^-6 / 3^4) = ? A. 3-2 B. 3^2 C. 3-10 D. 3^10…
  10. If (5/12)^-4 x (5/12)^3x = (5/12)^5 , then x=?A. -1 B. 1 C. 2 D. 3…
  11. (3/5)^0 = ? Choose the correct answer:A. 5/3 B. 3/5 C. 1 D. 0
  12. (-6/5)^-1 = ? Choose the correct answer:A. 6/5 B. -6/5 C. 5/6 D. -5/6…
  13. (-1/5)^3 = ? Choose the correct answer:A. -1/9 B. 1/9 C. -1/27 D. 1/27…
  14. Fill in the blanks. (i) 360000 written in standard form is.. (ii) 0.0000123 written in…
Exercise 2a
Question 1.

Evaluate:
(i) 4-3
(ii)
(iii)
(iv) (-3)-4
(v)


Answer:

Some basic formulas are:

Now,

(i)



(ii) = 25 = 32



(iii)




(iv) (-3)-4 =



(v)


Question 2.

Evaluate:

(i)

(ii)

(iii)

(iv)


Answer:

As we know from the rule of exponents that powers of the same base adds up to acquire new power.


(i)



(ii)



(iii)



(iv)



Question 3.

Evaluate:

(i)

(ii)

(iii)


Answer:

(i)


First we add the power of the same base,



Convert the powers in to positive numbers,





By cross multiplying we get,



= (3(4-3)) × (5(3-2)) = 3 × 15 = 15


(ii)





(iii)





Question 4.

Evaluate:

(i)

(ii)

(iii)


Answer:

(i)



(ii)




(iii)




Question 5.

Evaluate


Answer:

Consider ,

As we know,
Question 6.

Evaluate


Answer:

Consider ,

As we know,




Now take the LCM of 4 and 1 which is 4.
Question 7.

Evaluate [(5-1 × 3-1)-1 ÷ 6-1]
Answer:

For any number a ≠ 0
a-1 = 1/a
So,
[(5-1 × 3-1)-1 ÷ 6-1]

= [15 × 6]

= 90
Question 8.

Find the value of:
(i) (20 + 3-1) × 32
(ii) (2-1 × 3-1) ÷ 2-3
(iii)


Answer:

(i) (20 + 3-1) × 32

As we know that by the rule a0 = 1

So,

= 4 × 3(2-1)
= 4 × 3 = 12 Ans.

(ii) (2-1 × 3-1) ÷ 2-3



(iii)

= 22 + 32 + 42

= 4 + 9 + 16 = 29 Ans.


Question 9.

Find the value of x for which
Answer:


Consider the left side;



Given:



Comparing the powers;


-9 = 3x


=


x = -3
Question 10.

Find the value of x for which
Answer:

Given,




= 2x – 1 = -3


2x = -3 + 1 = -2


= x = -1
Question 11.

By what number should (-6)-1 be multiplied so that the product becomes 9-1?
Answer:

Let take that number be x;


(x) × (-6)-1 = 9-1



The greatest common divisor for the numerator and denominator is 3.
Question 12.

By what number should be divided so that the quotient may be?
Answer:

Let the number be x,
Question 13.

If , find the value of x.
Answer:

Given,



We know that,


25 = 5 × 5 = 52


125 = 5 × 5 × 5 = 53


= 53 = 5[(2x+1) -2] = 53


5[(2x+1)-2] = 5[2x-1] = 53


= 2x - 1 = 3


2x = 3 + 1 = 4



∴ x = 2
Exercise 2b
Question 1.

Write each of the following numbers in standard form:

(i) 57.36

(ii) 3500000

(iii) 273000

(iv) 168000000

(v) 4630000000000

(vi) 345 x105
Answer:

(i) 57.36 = 5.736 × 10


(ii) 3500000 = 35 × 105 = 3.5 × 106


(iii) 273000 = 273 × 103 = 2.73 × 105


(iv) 168000000 = 168 × 106 = 1.68 × 108


(v) 4630000000000 = 463 × 1010 = 4.63 × 1012


(vi) 345 × 105 = 34500000 =3.45 × 107
Question 2.

Write each of the following numbers in usual form:

(i) 3.74 × 105

(ii) 6.912 × 108

(iii) 4.1253 × 107

(iv) 2.5 × 104

(v) 5.17 × 108

(vi) 1.679 × 109
Answer:

(i) 3.74 × 105 = = 374 × 10(5-2) = 374 × 103 = 374000


(ii) 6.912 × 108 = = 6912 × 10(8-3) = 6912 × 105 = 691200000


(iii) 4.1253 × 107 = = 41253 × 10(7-4) = 41253 × 103 = 41253000


(iv) 2.5 × 104 = = 25 × 10(4-1) = 25 × 103 = 25000


(v) 5.17 × 106 = = 517 × 10(6-2) = 517 × 104 = 5170000


(vi) 1.679 × 109 = = 1679 × 10(9-3) = 1679 × 106 = 1679000000
Question 3.

The height of Mount Everest is 8848 m. Write it in standard form.
Answer:

Height of the Mount Everest = 8848m


If we wrights it in standard form we have,


8848 = 8.848 × 1000m = 8.848 × 103 m.
Question 4.

The speed of light is 300000000 m/sec. express it in standard form.
Answer:

Speed of the light = 300000000 m/sec


In standard for we will get,


300000000 = 3 × 100000000 m/sec = 3 × 108 m/sec
Question 5.

The distance from the earth to the sun is 149600000000 m. Write it in standard form.
Answer:

Distance from earth to sun = 149600000000 m


In standard form we have,


149600000000 = 1496 × 100000000


= 1.496 × 1000 × 100000000


= 1.496 × 103 × 108 = 1.496 × 1011 m.
Question 6.

Mass of earth is (5.97 x 1024) kg and mass of moon is (7.35 x 1022) kg. What is the total mass of the two?
Answer:

Given,


Mass of the earth = 5.97 × 1024 kg


Mass of the moon = 7.35 × 1022 kg


Now,


Mass of the earth = 5.97 × 1024 = 5.97 × 10(2+22) = 5.97 × 102 × 1022 = 597 × 1022


So,


We can also Wright the mass of the earth as 597 × 1022 kg


Sum of the masses of the earth and the moon;


= (597 × 1022) + (7.35 × 1022) = (597+7.35) × 1022 = 604.35 × 1022 kg


= 6.0435 × 100 × 1022 = 6.0435 × 102 × 1022 = 6.0435 × 10(2+22) = 6.0435 × 1024 kg
Question 7.

Write each of the following numbers in standard form:

(i) 0.0006

(ii) 0.00000083

(iii) 0.0000000534

(iv) 0.0027

(v) 0.00000165

(vi) 0.00000000689
Answer:

(i) 0.0006 = = 6 × 10-4


(ii) 0.00000083 = = 8.3 × 10(1-8) = 8.3 × 10-7


(iii) 0.0000000534 = = 5.34 × 10(2-10) = 5.34 × 10-8


(iv) 0.0027 = = 2.7 × 10(1-4) = 2.7 × 10-3


(v) 0.00000165 = = 1.65 × 10(2-8) = 1.65 × 10-6


(vi) 0.00000000689 = = 6.89 × 10(2-11) = 6.89 × 10-9
Question 8.

1 micron = m. Express it in standard form.
Answer:

1 micron = = 1 × 10-6 m.
Question 9.

Size of a bacteria = 0.0000004 m. Express it in standard form.
Answer:

Size of the bacteria = 0.0000004 m = = (4 × 10-7)m
Question 10.

Thickness of a paper = 0.03 mm. Express it in standard form.
Answer:

Thickness of paper = 0.03 mm = = (3 × 10-2) mm
Question 11.

Write each of the following numbers in usual form:

(i) 2.06x10-5

(ii) 5 x10-7

(iii) 6.82 x 10-6

(iv) 5.673x10-4

(v) 1.8 x10-2

(vi) 4.129 x10-3
Answer:

(i) 2.06 × 10-5 =






(ii) 5 × 10-7 =


= 0.0000005


(iii) 6.82 × 10-6 =





(iv) 5.673 × 10-4 =




(v) 1.8 × 10-2 =



= 0.018


(vi) 4.129 × 10-3 =



= 0.004129
Exercise 2c
Question 1.

The value of is
A.

B.

C.

D.


Answer:


Question 2.

The value of is
A. 12

B. 81

C.

D.
Answer:

(-3)-4 =


Question 3.

The value of is
A. -32

B.

C. 32

D.


Answer:

(-2)-5 =


Question 4.

The value of (2-5 ÷ 2-2) is
A.
B.
C.
D.


Answer:

Consider (2-5 ÷ 2-2),
We know,
For any non zero number "a"

So,
Question 5.

The value of is
A.

B.

C.

D.


Answer:




Question 6.

Choose the correct answer:


A.

B.

C. 29

D.


Answer:


= 22+32+42


= 4+9+16


= 29
Question 7.

Choose the correct answer:


A.

B.

C.

D.


Answer:





Question 8.

Choose the correct answer:

=?
A.

B. 16

C.

D. -16
Answer:





Question 9.

The value of x for which is
A. -1

B. 1

C. 2

D. 3
Answer:



3x-4 = 5


3x = 9


x = = 3
Question 10.

If , then x is equal to
A. -2

B. 0

C. 1

D. 2
Answer:



Now by cross multiplying,


(23x-1 + 10) × 1 = 6 × 7= 42


23x-1 = 42-10


23x-1 = 32


23x-1 = 25


3x-1 = 5


3x = 6


= 2


Therefore x = 2
Question 11.

Choose the correct answer:


A.

B.

C. 1

D. 0
Answer:

By using the law of exponents



Question 12.

Choose the correct answer:


A.

B.

C.

D. None of these
Answer:


Question 13.

Choose the correct answer:


A.

B.

C.

D.



Answer:


Question 14.

Choose the correct answer:


A.

B.

C.

D.


Answer:


Question 15.

3670000 in standard form is
A. 367 × 104

B. 36.7 × 105

C. 3.67 × 106

D. None of these
Answer:

3670000 = 367 × 104

The standard form is written as one decimal number with any integer power.
Therefore, 3670000 = 367 × 104


= 36.7 × 105


= 3.67 × 106


Thus, 3.67 × is the standard form.
Question 16.

0.0000463 in standard form is
A. 463 × 10–7

B. 4.63 × 10–5

C. 4.63 × 10–9

D. 46.3 × 10–6
Answer:

0.0000463 in standard form is written as:

0.0000463


= 0.463 × 10-4


= 4.63 × 10-5
Question 17.

0.000367 × 104 in usual form is
A. 3.67

B. 36.7

C. 0.367

D. 0.0367
Answer:

The usual form of 0.000367 × is written as:

0.000367 × 104


= 0.00367 × 103


=0.0367 × 102


= 0.367 × 101


= 3.67
Cce Test Paper-2
Question 1.

Evaluate

(i) 3-4

(ii) (-4)3

(iii)

(iv)


Answer:

(i) 3-4 =


(ii) (-4)3 = (-1)3 × (4)3 = -1 × 64 = -64


(iii)


(iv)


(v) Using the property we will get,


= 1
Question 2.

Evaluate:


Answer:

Consider

As we know (am)n = amn
Question 3.

Simplify:


Answer:








Question 4.

By what number should be divided so that the quotient is ?
Answer:

Suppose the number is x


So we have,
Question 5.

By what number should be multiplied so that the quotient is ?
Answer:

Let’s suppose the number is x


(-3)-1 × (x) = (6)-1





On cross multiplying:


(-x) × 6 = 1 × 3


-6x = 3


6x = -3
Question 6.

Express each of the following in standard form:

(i) 345

(ii) 180000

(iii) 0.000003

(iv) 0.000027
Answer:

(i) 345 = 3.45 × 100 = 3.45 × 102


(ii) 180000 = 18 × 1000 = 18 × 104 = 1.8 × 10 × 104 =1.8 × 10(1+4) =1.8 × 105


(iii) 0.000003 = = 3 × 10-6


(iv) 0.000027 = = 2.7 × 10(1-6) = 2.7 × 10-5
Question 7.

The value of is
A. -27

B. 9

C.

D.


Answer:

(-3)-3 =


Question 8.

The value of is
A.

B.

C.

D.


Answer:


Question 9.

Choose the corret answer:


A. 3-2

B. 32

C. 3-10

D. 310
Answer:



= 3-10
Question 10.

If , then x=?
A. -1

B. 1

C. 2

D. 3
Answer:



-4 + 3x = 5


3x = 5 + 4 = 9


= 3
Question 11.

Choose the correct answer:


A.

B.

C. 1

D. 0
Answer:

By the law of exponents


We will get,
Question 12.

Choose the correct answer:


A.

B.

C.

D.


Answer:


Question 13.

Choose the correct answer:


A.

B.

C.

D.


Answer:


Question 14.

Fill in the blanks.

(i) 360000 written in standard form is…..

(ii) 0.0000123 written in standard form is…..

(iii)

(iv) in usual form is…..

(v) in usual form is…..
Answer:

(i) 360000 written in standard form is 3.6 × 105


360000 = 36 × 104 = 3.6 × 10 × 104 = 3.6 × 10(1+4) = 3.6 × 105


(ii) 0.0000123 written in standard form is 1.23 × 10-5


0.0000123 =



= 1.23 × 10(2-7) = 1.23 × 10-5


(iii)



(iv) 3 × 10-3 in usual form is 0.003


3 × 10-3 = = 0.003


(v) 5.32 × 10-4 in usual form is 0.000532


5.32 × 10-4 = = 0.000532