12. Exponents and Powers – Class 8 Mathematics NCERT Chapter 12 Complete Guide (CBSE)
NCERT Class 8 Mathematics Chapter 12: Exponents and Powers – All Exercise Solutions | CBSE Board
Chapter 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 
.
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