NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.5

NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.5 - Number Systems

Edited By Vishal kumar | Updated on May 02, 2025 04:09 PM IST

The union of both rational and irrational numbers is called the real numbers. These real numbers are both positive and negative and denoted by the symbol $R$ . This chapter is about applying the Laws of Exponents to numbers with rational number exponents. The law of exponents simplifies the equation by manipulating the exponent and expression more efficiently. There are different ways of representing the same exponent. $a^{\frac{m}{n}}$ is the most common way which is used in the NCERT solutions for Class 9 Maths exercise 1.5. In problems, $a$ is a real number that is greater than zero, and $m$ and $n$ are the integers, and both $m$ and $n$ have no common factor other than one and in which is the denominator of the power is not zero because fraction cannot exist with denominator zero.

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NCERT Solutions for Class 9 Maths Chapter 1 – Number Systems Exercise 1.5
Access Number Systems Class 9 Chapter 1 Exercise: 1.5
Topics covered in Chapter 1 Number System: Exercise 1.5
NCERT Solutions of Class 9 Subject Wise
NCERT Subject-Wise Exemplar Solutions

NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.5 - Number Systems

NCERT Solutions for Class 9 Maths Exercise 1.5 deals with the idea of simplification of the real number with a power. Before exercise 1.5 Class 9 Maths we learnt about how to solve exponents with positive power when they are multiplied, and divided in a different condition when bases are the same or exponents is the same but in exercise 1.5 Class 9 Maths we are dealing with rational number as power along with the rational number power we are also introduced to the negative power and its application. In the NCERT solutions for Class 9 Maths exercise 1.5, there are four basic rules which have been used. These principles are the basis of these types of questions. There is only one way of solving them by applying these rules. The following exercises are also present, along with Class 9 Maths Chapter 1 exercise 1.5. Class 9th maths exercise 1.5 answers have been expertly crafted by our Subject Matter Experts. They are in simple language for easy understanding. This Class 9 Maths Chapter 1 Exercise 1.5 NCERT Book contains three questions with multiple parts. A PDF version is also available for free download, enabling offline use

NCERT Solutions for Class 9 Maths Chapter 1 – Number Systems Exercise 1.5

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Access Number Systems Class 9 Chapter 1 Exercise: 1.5

Q1 (i) Find : $64^{\frac{1}{2}}$

Solution:
Given number is $64^{\frac{1}{2}}$

Now, on simplifying it, we will get

$\Rightarrow 64^{\frac{1}{2}} = (8^{2})^{\frac{1}{2}} = 8$

Therefore, the answer is 8.

Q1 (ii) Find : $32^{\frac{1}{5}}$

Solution:
Given number is $32^{\frac{1}{5}}$

Now, on simplifying it, we will get

$\Rightarrow 32^{\frac{1}{5}} = (2^{5})^{\frac{1}{5}} = 2$

Therefore, the answer is 2.

Q1 (iii) Find : $125^{\frac{1}{3}}$

Solution:
Given number is $125^{\frac{1}{3}}$

Now, on simplifying it, we will get

$\Rightarrow 125^{\frac{1}{3}} = (5^{3})^{\frac{1}{3}} = 5$

Therefore, the answer is 5.

Q2 (i) Find : $9^{\frac{3}{2}}$

Solution:

Given number is $9^{\frac{3}{2}}$

Now, on simplifying it, we will get

$\Rightarrow 9^{\frac{3}{2}} = (3^{2})^{\frac{3}{2}} = 3^{3} = 27$

Therefore, the answer is 27.

Q2 (ii) Find : $32^{\frac{2}{5}}$

Solution:
Given number is $32^{\frac{2}{5}}$

Now, on simplifying it, we will get

$\Rightarrow 32^{\frac{2}{5}} = (2^{5})^{\frac{2}{5}} = 2^{2} = 4$

Therefore, the answer is 4.

Q2 (iii) Find : $16^{\frac{3}{4}}$

Solution:
Given number is $16^{\frac{3}{4}}$

Now, on simplifying it, we will get

$\Rightarrow 16^{\frac{3}{4}} = (2^{4})^{\frac{3}{4}} = 2^{3} = 8$

Therefore, the answer is 8.

Q2 (iv) Find : $125^{\frac{- 1}{3}}$

Solution:
Given number is $125^{\frac{- 1}{3}}$

Now, on simplifying it, we will get

$\Rightarrow 125^{\frac{- 1}{3}} = (5^{3})^{\frac{- 1}{3}} = 5^{- 1} = \frac{1}{5}$

Therefore, the answer is $\frac{1}{5}$ 15

Q3 (i) Simplify : $2^{\frac{2}{3}} {.2}^{\frac{1}{5}}$

Solution:
Given number is $2^{\frac{2}{3}} {.2}^{\frac{1}{5}}$

Now, on simplifying it, we will get

$\Rightarrow 2^{\frac{2}{3}} {.2}^{\frac{1}{5}} = 2^{\frac{2}{3} + \frac{1}{5}} = 2^{\frac{10 + 3}{15}} = 2^{\frac{13}{15}}$ $(∵ a^{m} . a^{n} = a^{m + n})$

Therefore, the answer is $2^{\frac{13}{15}}$

Q3 (ii) Simplify : ${(\frac{1}{3^{3}})}^{7}$

Solution:
Given number is ${(\frac{1}{3^{3}})}^{7}$

Now, on simplifying it, we will get

$\Rightarrow {(\frac{1}{3^{3}})}^{7} = \frac{1^{7}}{3^{3 \times 7}} = \frac{1}{3^{21}} = 3^{- 21}$ $(∵ (a^{m})^{n} = a^{m . n} a n d \frac{1}{a^{m}} = a^{- m})$

Therefore, the answer is $3^{- 21}$

Q3 (iii) Simplify : $\frac{11^{\frac{1}{2}}}{11^{\frac{1}{4}}}$

Solution:
Given number is $\frac{11^{\frac{1}{2}}}{11^{\frac{1}{4}}}$

Now, on simplifying it, we will get

$\Rightarrow \frac{11^{\frac{1}{2}}}{11^{\frac{1}{4}}} = 11^{\frac{1}{2} - \frac{1}{4}} = 11^{\frac{2 - 1}{4}} = 11^{\frac{1}{4}}$ $(∵ \frac{a^{m}}{a^{n}} = a^{m - n})$

Therefore, the answer is $11^{\frac{1}{4}}$

Q3 (iv) Simplify : $7^{\frac{1}{2}} {.8}^{\frac{1}{2}}$

Solution:
Given number is $7^{\frac{1}{2}} {.8}^{\frac{1}{2}}$

Now, on simplifying it we will get
$\Rightarrow 7^{\frac{1}{2}} {.8}^{\frac{1}{2}} = (7 \times 8)^{\frac{1}{2}} = 56^{\frac{1}{2}}$ $(∵ a^{m} . b^{m} = (a . b)^{m})$

Therefore, the answer is $56^{\frac{1}{2}}$

Also Read

Topics covered in Chapter 1 Number System: Exercise 1.5

In this topic, basic laws of exponents are covered, and these are as follows:

1. $a^{m} . a^{n} = a^{m + n}$

2. $(a^{m})^{n} = a^{m n}$

3. $\frac{a^{m}}{a^{n}}$ = $a^{m - n}$

4. $a^{m} . b^{m} = (a b)^{m}$

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NCERT Solutions of Class 9 Subject Wise

Students must check the NCERT solutions for Class 9 Maths and Science given below:

NCERT Subject-Wise Exemplar Solutions

Students must check the NCERT exemplar solutions for Class 9 Maths and Science given below:

Frequently Asked Questions (FAQs)

1. In Class 9 Mathematics chapter 1 exercise 1.6, how many solved examples are there?

One solved example is there in Class 9 Maths chapter 1 exercise 1.6

2. What number of questions are there in chapter 1 exercise 1.6 of Class 9 Maths?

Three questions are there in chapter 1 exercise 1.6 of Class 9 Maths. The question one has three subparts, question two has four sub-parts and question three has four subparts.

3. What kinds of questions may be found in NCERT Solutions for Class 9 Maths chapter 1 Exercise 1.6?

Two types of questions are there in chapter 1 exercise 1.6 of Class 9 Math. Firstly we have a question in which we have to find a solution to the problem using the law of exponent and secondly we have a question in which we have to simplify.

Also Read

NCERT Solutions for Class 9 Maths Chapter 12 Exercise 12.1 - Statistics

NCERT Solutions for Class 9 Maths Chapter 11 Exercise 11.4 - Surface Area and Volumes

NCERT Solutions for Class 9 Maths Chapter 11 Exercise 11.3- Surface Area and Volumes

NCERT Solutions for Class 9 Maths Chapter 11 Exercise 11.2 - Surface Area and Volumes

NCERT Solutions for Class 9 Maths Chapter 11 Exercise 11.1 - Surface Area and Volumes

NCERT Solutions for Class 9 Maths Chapter 9 Exercise 9.3 - Circles

NCERT Class 9 Science Notes - Download Chapter-wise PDFs

NCERT Class 9 Notes - Download Subject Wise PDF Notes

NCERT Class 9 Maths Chapter 5 Notes Introduction To Euclid’s Geometry - Download PDF

NCERT Class 9 Maths Chapter 1 Notes Number System - Download Free PDF

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Triangles Class 9th Notes - Free NCERT Class 9th Maths Chapter 7 Notes - Download PDF

NCERT Exemplar Class 9 Solutions - Subject Wise Problems with Solutions

NCERT Exemplar Class 9 Maths Solutions Chapter 2 Polynomials

NCERT Exemplar Class 9 Maths Solutions Chapter 6 Lines and Angles

NCERT Exemplar Class 9 Maths Solutions Chapter 5 Introduction to Euclids Geometry

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NCERT Exemplar Class 9 Science Solutions Chapter 14 Natural Resources

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