Looking for accurate SEBA Class 9 Maths Exercise 1.5 (Number Systems) textual solutions for the 2026–27 academic year? Access complete step-by-step solutions covering the laws of exponents for real numbers, evaluating fractional power expressions, simplifying exponential bases, and applying negative and product exponent rules to score top marks in your annual exams.
EXERCISE 1.5
1. Find:
(i) 64¹ᐟ²
= (8²)¹ᐟ²
= 8²ˣ¹ᐟ²
= 8¹
= 8
(ii) 32¹ᐟ⁵
= (2⁵)¹ᐟ⁵
= 2⁵ˣ¹ᐟ⁵
= 2¹
= 2
(iii) 125¹ᐟ³
= (5³)¹ᐟ³
= 5³ˣ¹ᐟ³
= 5¹
= 5
2. Find:
(i) 9³ᐟ²
= (3²)³ᐟ²
= 3²ˣ³ᐟ²
= 3³
= 27
(ii) 32²ᐟ⁵
= (2⁵)²ᐟ⁵
= 2⁵ˣ²ᐟ⁵
= 2²
= 4
(iii) 16³ᐟ⁴
= (2⁴)³ᐟ⁴
= 2⁴ˣ³ᐟ⁴
= 2³
= 8
(iv) 125⁻¹ᐟ³
= (5³)⁻¹ᐟ³
= 5³ˣ⁽⁻¹ᐟ³⁾
= 5⁻¹
= 1/5
SEBA Class 9 Maths Exercise 1.5 Solutions
3. Simplify:
(i) 2²ᐟ³ · 2¹ᐟ⁵
= 2²ᐟ³ ⁺ ¹ᐟ⁵
= 2⁽¹⁰⁺³⁾ᐟ¹⁵
= 2¹³ᐟ¹⁵
(ii) (1/3³)⁷
= (3⁻³)⁷
= 3⁻³ˣ⁷
= 3⁻²¹ or 1/3²¹
(iii) 11¹ᐟ² / 11¹ᐟ⁴
= 11¹ᐟ² ⁻ ¹ᐟ⁴
= 11⁽²⁻¹⁾ᐟ⁴
= 11¹ᐟ⁴
(iv) 7¹ᐟ² · 8¹ᐟ²
= (7 × 8)¹ᐟ²
= 56¹ᐟ²
Class 9 Maths Chapter 1 Exercise 1.5 Question Answer SEBA 2026-27
| Column I | Column II |
| (P) 32¹ᐟ⁵ | 1) 5 |
| (Q) 81¹ᐟ⁴ | 2) 1 |
| (R) 625¹ᐟ⁴ | 3) 2 |
| (S) 5096⁰ | 4) 3 |
Choose the correct option:
P Q R S
(A) 4) 3) 2) 1)
(B) 3) 1) 4) 2)
(C) 3) 4) 1) 2)
(D) 2) 3) 4) 1)
soln: (P) 32¹ᐟ⁵ = (2⁵)¹ᐟ⁵ = 2 => Match: 3)
(Q) 81¹ᐟ⁴ = (3⁴)¹ᐟ⁴ = 3 => Match: 4)
(R) 625¹ᐟ⁴ = (5⁴)¹ᐟ⁴ = 5 => Match: 1)
(S) 5096⁰ = 1 => Match: 2)
Matching sequence:
P -> 3), Q -> 4), R -> 1), S -> 2)
Correct Option: (C)
Laws of Exponents Class 9 SEBA Ex 1.5 Solutions
5. Consider the following statements A to D. Choose the option that represents the correct increasing sequence of terms.
A) ³√2, ⁶√3, ⁹√4
B) ⁹√4, ⁶√3, ³√2
C) ⁶√3, ⁹√4, ³√2
D) ³√2, ⁹√4, ⁶√3
soln: Given terms: ³√2, ⁶√3, ⁹√4
Expressing exponents with fractional powers:
³√2 = 2¹ᐟ³
⁶√3 = 3¹ᐟ⁶
⁹√4 = 4¹ᐟ⁹ = (2²)¹ᐟ⁹ = 2²ᐟ⁹
Taking the LCM of power denominators (3, 6, 9) = 18:
2¹ᐟ³ = 2⁶ᐟ¹⁸ = (2⁶)¹ᐟ¹⁸ = 64¹ᐟ¹⁸
3¹ᐟ⁶ = 3³ᐟ¹⁸ = (3³)¹ᐟ¹⁸ = 27¹ᐟ¹⁸
2²ᐟ⁹ = 2⁴ᐟ¹⁸ = (2⁴)¹ᐟ¹⁸ = 16¹ᐟ¹⁸
Comparing bases: 16 < 27 < 64 => 16¹ᐟ¹⁸ < 27¹ᐟ¹⁸ < 64¹ᐟ¹⁸ => ⁹√4 < ⁶√3 < ³√2
Correct Option: (B)
SEBA Class 9 Maths Chapter 1 Exercise 1.5 Textbook Answers
6. Mathematics teacher asks Rabi and Rohan to make a right angle by match sticks. Both of them put 1 match stick horizontally and the other in vertical direction as shown in the figure (i). Then teacher joins the open ends of the right angle by a string as shown in the figure (ii). Teacher asks them to find the length of the string, if each match stick is of unit length. Pragyam comes forward and replies, the length of the string can be found by using Pythagoras theorem and it is equal to √(1² + 1²) = √2 units. Using your knowledge about numbers, answer the following questions.
(i) √2 is
(A) A Rational number
(B) An Integer
(C) A Whole number
(D) An Irrational number
Answer: (D) An Irrational number
(ii) The decimal representation of a rational number cannot be.
(A) terminating
(B) non terminating
(C) non terminating repeating
(D) non terminating non repeating
Answer: (D) non terminating non repeating
(iii) The decimal representation of an irrational numbers is
(A) terminating
(B) non terminating recurring
(C) non terminating non recurring
(D) non terminating
Answer: (C) non terminating non recurring
(iv) The sum of any two irrational numbers is
(A) Always an integer
(B) Always an irrational number
(C) Always a rational number
(D) Either rational or irrational
Answer: (D) Either rational or irrational
Class 9 Maths Laws of Exponents Real Numbers Solutions
📐 Updated Solutions Notice: This page features complete, step-by-step SEBA Class 9 Mathematics Chapter 1 (Number Systems) Exercise 1.5 Textual Solutions updated for the 2026–27 academic session. All evaluations of fractional exponents, power-of-a-power simplifications, and zero/negative index rules strictly follow the latest revised Assam Board (SEBA) curriculum.
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