NCERT Class 9 Maths Chapter 1 Number Systems Exercise 1.6

Chapter 1 Number Systems Exercise 1.6

Question 1: Find:
i) 64^1/2
ii)32^1/5
iii) 125^1/3
Answer:
i)
= (8²)^1/2
by (a^m)ⁿ = a^mn
= 8^{2 × 1/2}
= 8

ii)
= (2⁵)^1/5
by (a^m)ⁿ = a^mn
= 2^{5 × 1/5}
= 2

iii)
= (5³)^1/3
by (a^m)ⁿ = a^mn
= 5^{3 × 1/3}
= 5

Question 2: Find:
i) 9^3/2
ii) 32^2/5
iii) 16^3/4
iv) 125^-1/3
Answer:
i)
= (3²)^3/2
by (a^m)ⁿ = a^mn
= 3^{2 × 3/2}
= 3³
= 27

ii)
= (2⁵)^2/5
by (a^m)ⁿ = a^mn
= 2^{5 × 2/5}
= 2²
= 4

iii)
= (2⁴)^3/4
by (a^m)ⁿ = a^mn
= 2^{4 × 3/4}
= 2³
= 8

iv)
= (5³)^-1/3
by (a^m)ⁿ = a^mn
= 5^{3 × -1/3}
= 5^-1
by a^-n = 1/aⁿ
= 1/5

Question 3: Simplify:
i) 2^2/3 × 2^1/5
ii) (1/3³)⁷
iii) 11^1/2/11^1/4
iv) 7^1/2 × 8^1/2
Answer:
i) 2^2/3 × 2^1/5
by a^m × aⁿ = a^{m + n}
= 2^{2/3 + 1/5} (2/3 + 1/5 = 10 + 3/15 = 13/15)
= 2^13/15
= ¹⁵√2¹³

ii) (1/3³)⁷
by (a^m)ⁿ = a^mn
= (1/3³)⁷
= 1/3^{3 × 7}
= 1/3²¹
by a^-n = 1/aⁿ
= 3^-21

iii) 11^1/2/11^1/4
By a^m/aⁿ = a^{m - n}
= 11(^{1/2 – 1/4})
= 11^{2/4 – 1/4}
= 11^1/4
= ⁴√11

iv) 7^1/2 × 8^1/2
by a^m × b^m = (ab)^m
= (7 × 8)^1/2
= 56^1/2
= √56