12. Exponents and Powers

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Law of exponents : If  and  are non zero integers and are any integers .

(i)  

(ii)     

(iii) 

(iv)   

(v) 

(vi)

(vii)

(viii)  

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Exercise 12.1

1. Evaluate :   

(i)  (ii)     (iii)  

Solution:  (i) We have ,

    

(ii) We have,

 

(iii) We have ,

 

2. Simplify and express the result in power notation with positive exponent.

(i) 

(ii)  

(iii) 

(iv)  

(v)    

Solution: (i) We have,

(ii) We have, 

(iii) We have,

(iv) We have ,

(v) We have, 

3. Find the value of .

(i) 

(ii)  

(iii) 

(iv)   

(v) 

Solution: (i) We have, 

(ii) We have,

(iii) We have,

 

(iv) We have, 

(v) We have , 

4. Evaluate :

(i)     

(ii) 

Solution: (i) We have, 

     

(ii) We have , 

5. Find the value of  for which

Solution: We have,

The value of  is 2 .

6. Evaluate  : 

(i)         

(ii)  

Solution: (i) We have,

 

(ii) We have, 

  

7. Simplify :

(i)        

(ii)  

Solution: (i) We have,

  

(ii) We have,

 

Exercise 12.2

1. Express the following numbers in standard form.
(i) 0.0000000000085      

(ii) 0.00000000000942        

(iii) 6020000000000000   

(iv) 0.00000000837       

(v) 31860000000

Solution: (i) We have, 

 

(ii) We have, 

(iii) We have,

 

(iv) We have, 

(v) We have ,

2. Express the following numbers in usual form.
(i) 3.02 ×  

(ii) 4.5 ×

(iii) 3 ×
(iv) 1.0001 × 

(v) 5.8 ×

(vi) 3.61492 ×

Solution: (i) We have,

(ii) We have, 

 

(iii) We have,

(iv)We have,

 

(v) We have,

 

(vi) We have,

 

3. Express the number appearing in the following statements in standard form.
(i) 1 micron is equal to  m.
(ii) Charge of an electron is 0.000,000,000,000,000,000,16 coulomb.
(iii) Size of a bacteria is 0.0000005 m
(iv) Size of a plant cell is 0.00001275 m
(v) Thickness of a thick paper is 0.07 mm

Solution: (i) 1 micron is equal to   m

(ii) Charge of an electron is 0.000,000,000,000,000,000,16 coulomb.

(iii) Size of a bacteria is 0.0000005 m
A bacteria

(iv) Size of a plant cell is 0.00001275 m.

 

4. In a stack there are 5 books each of thickness 20mm and 5 paper sheets each of thickness 0.016 mm. What is the total thickness of the stack.

Solution:  Thickness of 5 books  

Thickness of 5 paper sheets

The total thickness of the stack