8TH MATHS PART 2 CHAPTER 2 EXPONENTS AND POWERS-3 EXERCISE 2.1
NCERT MATHS PART 2 CHAPTER 2
EXPONENTS AND POWERS EXERCISE 2.1
SOLUTIONS
Question 1:
Evaluate
(i) 3−2 (ii) (−4)−2 (iii) 
ANSWER:
(i) 
(ii) 
(iii) 
Question 2:
Simplify and express the result in power notation with positive exponent.
(i) 
(ii) 
(iii) 
(iv) 
(v) 
ANSWER:
(i) (−4)5 ÷ (−4)8 = (−4)5 − 8 (am ÷ an = am − n)
= (− 4)−3
(ii) 
(iii) 
(iv) (3− 7 ÷ 3−10) × 3−5 = (3−7 − (−10)) × 3−5 (am ÷ an = am − n)
= 33 × 3−5
= 33 + (− 5) (am × an = am + n)
= 3−2
(v) 2−3 × (−7)−3 = 
Question 3:
Find the value of.
(i) (30 + 4−1) × 22 (ii) (2−1 × 4−1) ÷2−2
(iii) 
(iv) (3−1 + 4−1 + 5−1)0
(v) 
Find the value of.
(i) (30 + 4−1) × 22 (ii) (2−1 × 4−1) ÷2−2
(iii) (iv) (3−1 + 4−1 + 5−1)0
(v)
ANSWER:
(i) 
(ii) (2−1 × 4−1) ÷ 2− 2 = [2−1 × {(2)2}− 1] ÷ 2− 2
= (2− 1 × 2− 2) ÷ 2− 2 
= 2−1+ (−2) ÷ 2−2 (am × an = am + n)
= 2−3 ÷ 2−2
= 2−3 − (−2) (am ÷ an = am − n)
= 2−3 + 2 = 2 −1
(iii) 
(iv) (3−1 + 4−1 + 5−1)0 
= 1 (a0 = 1)
(v) 
(i)
(ii) (2−1 × 4−1) ÷ 2− 2 = [2−1 × {(2)2}− 1] ÷ 2− 2
= (2− 1 × 2− 2) ÷ 2− 2
= 2−1+ (−2) ÷ 2−2 (am × an = am + n)
= 2−3 ÷ 2−2
= 2−3 − (−2) (am ÷ an = am − n)
= 2−3 + 2 = 2 −1
(iii)
(iv) (3−1 + 4−1 + 5−1)0
= 1 (a0 = 1)
(v)
Question 4:
Evaluate (i) 
(ii) 
Evaluate (i) (ii)
ANSWER:
(i) 
(ii) 
(i)
(ii)
Question 5:
Find the value of m for which 5m ÷5−3 = 55.
ANSWER:
5m ÷ 5−3 = 55
5m − (− 3) = 55 (am ÷ an = am − n)
5m + 3 = 55
Since the powers have same bases on both sides, their respective exponents must be equal.
m + 3 = 5
m = 5 − 3
m = 2
Question 6:
Evaluate (i) 
(ii) 
ANSWER:
(i) 
(ii) 
Question 7:
Simplify. (i) 
(ii) 
ANSWER:
(i) (i) 
(ii) 
