Important questions for Exponents Class 8 Chapter 12 CBSE

Question 1  
Evaluate

1. 2 ^-2
2. (- 2) ^{- 2}
3.  (3/2)^-5   

Answer
As we know that
b^-n= 1/bⁿ
(i)  2^-2  =  1/ 2²  =1/4
(ii) (-2)^-2  = 1/(-2)²= 1/4
(iii) (3/2)^-5   =3-⁵/ 2^-5 =2⁵/3⁵   = 32/243
Question 2  
 Simplify and express the result in power notation with positive exponent.
(i) (-2)⁵ ÷   (-2)⁴
(ii) (1/2)² × (2/5)²
(iii) (-5)² × (3/5)

Answer
(i)  (-2)⁵ ÷   (-2)⁴
= (-2)⁵ / (-2)⁴
= (-2)^5-4
=-2
(ii) (1/2)² × (2/5)²
=   (1/4) X   (4/25)
= 1/25
iii) (-5)² × (3/5)
=25 × (3/5) =15
Question 3
Find the value of.

1. (4⁰ + 4 ^{- 1}) × 2²
2.  (3 ^{- 1} × 9 ^{- 1})  ÷ 3 ^{- 2}
3. (11 ^{- 1} + 12 ^{- 1} + 13 ^{- 1})⁰

Answer

1. (4⁰ + 4 ^{- 1}) × 2² = (1+1/4) × 4
   = 4+1=5
   
2. (3 ^{- 1} × 9 ^{- 1})  ÷ 3 ^{- 2} = [(1/3) × (1/9)] ÷ (1/9)
        =1/3
   

         3. (11 ^{- 1} + 12 ^{- 1} + 13 ^{- 1})⁰
            =1   as  a⁰ =1
 Question 4
Find the value of   x here
(11/9)³   x  (9/11)⁶  = (11/9)^2x-1

Answer
(11/9)³   x (11/9)^-6  =  (11/9)^2x-1
(11/9)^3-6  =  (11/9)^2x-1
-3=2x-1
Or
x=-1


Question 5
Find the value of m for which 2^m   ÷  2^-4 = 4⁵
Answer
2^m   ÷   2^-4 = 4⁵
2^m × (1/2^-4)  = 2¹⁰
2^m+4 =2¹⁰
So  m+4=10
m=6
Question 6
Express the following numbers in standard form.
(i) 0.0000000015 (ii) 0.00000001425
(iii) 102000000000000000

Answer

1. 0.0000000015 =1.5 ×10^-9
   
2. 0.00000001425
   =1.425×10^-8

     3. 102000000000000000
=1.02×10¹⁷
Question 7
Express the following numbers in usual form.
(i) 34.02 x 10^-5 (ii) 9.5 x 10⁵
(iii) 9 x 10^-4 (iv) 2.0001 x 10⁸

Answer

1. 34.02 x 10^-5 = .0003402
   

      2. 9.5 x 10⁵
     =950000
    3. 9 x 10^-4
    =.0009
    4. 2.0001 x 10⁸
=200010000

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