Number Systems l Exercise 1.5 l Class 9 l NCERT Solutions

NCERT Class 9 Maths Chapter 1 Number Systems Exercise 1.5 Solutions | Step-by-Step Explanation

Chapter: Number Systems
Class: 9 (CBSE)
Exercise: 1.5
Board: CBSE 2026

Important Laws of Exponents Used

• a^m × aⁿ = a^m+n
• (a^m)ⁿ = a^mn
• a^m / aⁿ = a^m−n
• a^−m = 1 / a^m
• a^1/n = nth root of a

Exercise 1.5 Solutions

Question 1: Find

(i) 64^1/2

= √64 = 8

(ii) 32^1/5

32 = 2⁵

= (2⁵)^1/5

= 2

(iii) 125^1/3

125 = 5³

= (5³)^1/3

= 5

Question 2: Find

(i) 9^3/2

= (√9)³

= 3³

= 27

(ii) 32^2/5

32 = 2⁵

= (2⁵)^2/5

= 2²

= 4

(iii) 16^3/4

16 = 2⁴

= (2⁴)^3/4

= 2³

= 8

(iv) 125^−1/3

125 = 5³

= (5³)^−1/3

= 5⁻¹

= 1/5

Question 3: Simplify

(i) 2^2/3 × 2^1/5

Using a^m × aⁿ = a^m+n

= 2^{(2/3 + 1/5)}

LCM of 3 and 5 = 15

= 2^{(10/15 + 3/15)}

= 2^13/15

(ii) (1 / 3³)⁷

= 1⁷ / (3³)⁷

= 1 / 3²¹

(iii) 11^1/2 / 11^1/4

Using a^m / aⁿ = a^m−n

= 11^{(1/2 − 1/4)}

= 11^{(2/4 − 1/4)}

= 11^1/4

(iv) 7^1/2 × 8^1/2

= (7 × 8)^1/2

= 56^1/2

= √56

= √(4 × 14)

= 2√14

Final Summary

• Fractional exponents represent roots.
• Negative exponents represent reciprocals.
• Always apply exponent laws carefully.
• Convert numbers into prime powers when possible.

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