Number System Class 9 Chapter 1 Ex 1.5 NCERT Solutions

Number System Class 9 Exercise 1.5 Chapter 1 extends the application of exponent rules to more complex problems. It reinforces concepts of rational exponents and shows how to apply them in expressions. 

NCERT Maths Class 9 Number System Exercise 1.5 solutions provide clear and  step-by-step solutions to solve problems easily. They include worked examples that explain how to handle rational exponents, simplify expressions, and avoid common errors. 

Class 9 Chapter 1 Number System Exercise 1.5 Questions

Class 9 Chapter 1 Number System Exercise 1.5 Questions focus on applying rational exponents to real numbers. Practising these questions with clear solutions helps develop speed and accuracy. NCERT questions along with step by step solutions are given here:

1. Find:

(i)64 1/2

Solution: 64 1/2 = (8×8) 1/2 = (8 2 ) ½ = 8 1 [⸪2×1/2 = 2/2 =1] = 8

(ii)32 1/5

Solution: 32 1/5 = (2 5 ) 1/5 = (2 5 ) ⅕ = 2 1 [⸪5×1/5 = 1] = 2

(iii)125 1/3

Solution: (125) 1/3 = (5×5×5) 1/3 = (5 3 ) ⅓ = 5 1 (3×1/3 = 3/3 = 1) = 5

2. Find:

(i) 9 3/2

Solution: 9 3/2 = (3×3) 3/2 = (3 2 ) 3/2 = 3 3 [⸪2×3/2 = 3] =27

(ii) 32 2/5

Solution: 32 2/5 = (2×2×2×2×2) 2/5 = (2 5 ) 2⁄5 = 2 2 [⸪5×2/5= 2] = 4

(iii)16 3/4

Solution: 16 3/4 = (2×2×2×2) 3/4 = (2 4 ) 3⁄4 = 2 3 [⸪4×3/4 = 3] = 8

(iv) 125 -1/3

Solution: 125 -1/3 = (5×5×5) -1/3 = (5 3 ) -1⁄3 = 5 -1 [⸪3×-1/3 = -1] = 1/5

3. Simplify :

(i) 2 2/3 ×2 1/5

Solution: 2 2/3 ×2 1/5 = 2 (2/3)+(1/5) [⸪Since, a m ×a n =a m+n ____ Laws of exponents] = 2 13/15 [⸪2/3 + 1/5 = (2×5+3×1)/(3×5) = 13/15]

(ii) (1/3 3 ) 7

Solution: (1/3 3 ) 7 = (3 -3 ) 7 [⸪Since,(a m ) n = a m x n ____ Laws of exponents] = 3 -21

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

Solution: 11 1/2 /11 1/4 = 11 (1/2)-(1/4) = 11 1/4 [⸪(1/2) – (1/4) = (1×4-2×1)/(2×4) = 4-2)/8 = 2/8 = ¼ ]

(iv) 7 1/2 ×8 1/2

Solution: 7 1/2 ×8 1/2 = (7×8) 1/2 [⸪Since, (a m ×b m = (a×b) m ____ Laws of exponents] = 56 1/2

NCERT Maths Class 9 Number System Exercise 1.5 PDF

NCERT solutions for class 9 Maths Number System Exercise 1.5 PDF includes step-by-step solutions. This makes it easier for students to revise rational exponent problems anytime. The PDF also explains simplified expressions to help students prepare effectively.

By regularly using this resource, you can improve your understanding of Number System Class 9 concepts and confidently handle questions related to rational exponent questions in the exam.

NCERT Maths Class 9 Number System Exercise 1.1 PDF

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