Exercise 12.1
Question 1.
Evaluate:
(i) 
(ii) 
(iii) 
Solution :
(i) = 1/3²
= 1/9
(ii) 
= 1/16
(iii) = 
= 
= 32
Question 2.
Simplify and express the result in power notation with positive exponent:
(i) 
(ii) 
(iii) 
(iv) 
(v) 
Solution :
(i)
= 
= 
(ii) 
= 
(iii) 
= 
= 
= 
(iv) 
= .png)
= 
= 
= 
Question 3.
Find the value of:
Solution :
Question 4.
Evaluate:
Solution :
= 1/10 × 1/6 = 1/60
Question 5.
Find the value of m for which 
Solution :
Comparing exponents both sides, we get
m+3 = 5
m = 5 – 3
m = 2
Question 6.
Evaluate:
Question 7.
Simplify:
NCERT Solutions for Class 8 Maths Exercise 12.2
Question 1.
Express the following numbers in standard form:
(i) 0.0000000000085
(ii) 0.00000000000942
(iii) 6020000000000000
(iv) 0.00000000837
(v) 31860000000
Solution :
(i) 0.0000000000085
= 0.0000000000085 
= 
(ii) 0.00000000000942
= 0.00000000000942
=
(iii) 6020000000000000
= 6020000000000000 
= 
(iv) 0.00000000837
= 0.00000000837 
= 
(v) 31860000000 = 31860000000 .png)
= 
Question 2.
Express the following numbers in usual form :
Solution :
Question 3.
Express the number appearing in the following statements in standard form :
(i)1 micron is equal to 1/ 1000000 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 if a thick paper is 0.07 mm.
Solution :
(i) 1 micron
= 
m
(ii)Charge of an electron is
0.00000000000000000016 coulombs.
= 0.00000000000000000016 
= 
coulomb
(iii) Size of bacteria = 0.0000005
= 
= 
m
(iv) Size of a plant cell is 0.00001275 m
= 0.00001275 
= 
m
(v) Thickness of a thick paper = 0.07 mm
= 7/100mm = 
mm
Question 4.
In a stack there are 5 books each of thickness 20 mm and 5 paper sheets each of thickness 0.016 mm. What is the total thickness of the stack?
Solution :
Thickness of one book = 20 mm
Thickness of 5 books = 20 × 5 = 100 mm
Thickness of one paper = 0.016 mm
Thickness of 5 papers = 0.016 × 5
= 0.08 mm
Total thickness of a stack = 100 + 0.08
=100.08 mm
= 100.08 
mm