Exponents and Powers-NCERT Solutions

Class VIII Math

NCERT Solution for Exponents and Powers
EXERCISE: 12.1 (Page 197)
Q1.   Evaluate:
           (i) 3�2
(ii) (�4)�2
(iii)
Q2.   Simplify and express the result in power notation with positive exponent.
           
           
Q3.   Find the value of:
           
           
           
Q5.   Find the value of m for which 5m ÷ 5–3 = 55.
Sol.    ∵ am ÷ an = am – n
           ∴ L.H.S = 5m ÷ 5–3
           = 5m–(–3) = 5m + 3
           Now 5m + 3 = 55
           Since, bases 5 are equal, therefore exponents are also equal.
           i.e. m + 3 = 5
           or m = 5 – 3 = 2
           Thus, the required value of m is 2.
EXERCISE: 12.2 (Page 200)
Q1.   Express the following numbers in standard form.
           (i) 0.0000000000085
(ii) 0.00000000000942
           (iii) 6020000000000000
(iv) 0.00000000837
           (v) 31860000000
Q2.   Express the following numbers in usual form.
           (i) 3.02 � 10�6
(ii) 4.5 � 104
(iii) 3 � 10�8
           (iv) 1.0001 � 109
(v) 5.8 � 1012
(vi) 3.61492 � 106
Sol. (i) 3.02 � 10�6 = 302 � 10�2 � 10�6
                  = 302 � 10�8
           
           
Q3.   Express the number appearing in the following statements in standard form.
           (i) 1 micron is equal to
           (ii) Charge of an electron is 0.000,000,000,000,000,000,16 coulomb.
           (iii) Size of a plant cell is 0.00001275 m.
           (iv) Size of a plant cell is 0.00001275 m.
           (v) Thickness of a thick paper is 0.07 mm.
Sol.
           
Q4.   In a stack there are 5 books each of thickness 20 mm and 5 paper sheets each of thickness 0.016mm. What is the total thickness of the stack?
Sol.    ∵ Thickness of one book = 20 mm
           ∴ Thickness of 5 books = 5 × 20 mm = 100 mm
           Again,
                   Thickness of 1 paper sheet = 0.016 mm
           ∴ Thickness of 5 paper sheets = 5 × 0.016 mm
           = 0.080 m
           ∴ Total thickness = 100 mm + 0.080 mm
                   = 100.08 mm = 1.0008 × 102 mm