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NCERT Solutions for Exercise 1.6 Class 9 Maths Chapter 1 - Number Systems

NCERT Solutions for Exercise 1.6 Class 9 Maths Chapter 1 - Number Systems

Edited By Vishal kumar | Updated on Oct 03, 2023 09:23 AM IST

NCERT Solutions for Class 9 Maths Chapter 1: Number Systems Exercise 1.6- Download Free PDF

NCERT Solutions for Class 9 Maths Chapter 1 - Number Systems Exercise 1.6- NCERT Solutions for Class 9 Maths Exercise 1.6 deals with the idea of simplification of the real number with power. Before exercise 1.6 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 1.6 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.

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  1. NCERT Solutions for Class 9 Maths Chapter 1: Number Systems Exercise 1.6- Download Free PDF
  2. NCERT Solutions for Class 9 Maths Chapter 1 – Number Systems Exercise 1.6
  3. Access Number Systems Class 9 Chapter 1 Exercise: 1.6
  4. More About NCERT Solutions for Class 9 Maths Exercise 1.6: Laws of Exponents for Real Numbers
  5. Benefits of NCERT Solutions for Class 9 Maths Exercise 1.6:
  6. key Features of Exercise 1.6 Class 9 Maths
  7. NCERT Solutions of Class 10 Subject Wise
  8. Subject Wise NCERT Exemplar Solutions
NCERT Solutions for Exercise 1.6 Class 9 Maths Chapter 1 - Number Systems
NCERT Solutions for Exercise 1.6 Class 9 Maths Chapter 1 - Number Systems

In NCERT solutions for Class 9 Maths exercise 1.6, 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 1.6.

9th class maths exercise 1.6 answers have been expertly crafted by Careers360 subject experts. They are in simple language for easy understanding. This class 9 maths chapter 1 exercise 1.6 contains three questions with multiple parts. A PDF version is available for free download, enabling offline use.

NCERT Solutions for Class 9 Maths Chapter 1 – Number Systems Exercise 1.6

Download PDF


Access Number Systems Class 9 Chapter 1 Exercise: 1.6

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

Answer:

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, answer is 8

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

Answer:

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}}

Answer:

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}}

Answer:

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}}

Answer:

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}}

Answer:

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}}

Answer:

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}

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

Answer:

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} \left ( \because a^n.a^m = a^{n+m} \right )

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

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

Answer:

Given number is \left (\frac{1}{3^{3}} \right )^{7}

Now, on simplifying it we will get

\Rightarrow \left ( \frac{1}{3^3} \right )^7= \frac{1^7}{3^{3\times7}} = \frac{1}{3^{21}} = 3^{-21} \left ( \because (a^n)^m = a^{n.m} \ and \ \frac{1}{a^m}= a^{-m}\right )

Therefore, the answer is 3^{-21}

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

Answer:

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} \left ( \because \frac{a^n}{a^m}= a^{n-m}\right )
Therefore, the answer is 11^{\frac{1}{4}}

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

Answer:

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\times8)^{\frac{1}{2}} = 56^{\frac{1}{2}} \left ( \because a^n.b^n=(a.b)^n\right )
Therefore, the answer is 56^{\frac{1}{2}}

More About NCERT Solutions for Class 9 Maths Exercise 1.6: Laws of Exponents for Real Numbers

The NCERT book Class 9 Maths Exercise 1.6 is about applying the Laws of Exponents on numbers with rational number exponents. 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 1.6. 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 the n which is the denominator of the power is not zero because fraction cannot exist with denominator zero.

Also Read| Number Systems Class 9 Notes

Benefits of NCERT Solutions for Class 9 Maths Exercise 1.6:

  • NCERT solutions for Class 9 Maths exercise 1.6 help us establish our fundamental understanding of numbers and their properties.

  • By solving the NCERT solutions for Class 9 Maths chapter 1 exercise 1.6 builds a strong foundation of mathematical understanding as well as confidence in approaching new topics in higher grades.

  • NCERT syllabus Class 9 Maths exercise 1.6 will assist us in understanding how to conduct operations on real numbers, which will aid us in future courses.

key Features of Exercise 1.6 Class 9 Maths

  1. Subject Expert Solutions: The 9th class maths exercise 1.6 answers are crafted by subject matter experts. This ensures accuracy and clarity in explanations.

  2. Detailed Explanations: Each class 9 maths chapter 1 exercise 1.6 solution is accompanied by detailed explanations, making it easier for students to understand the concepts and problem-solving techniques.

  3. Step-by-Step Format: The exercise 1.6 class 9 maths solutions are presented in a step-by-step format, helping students follow the solution process.

  4. Multiple Questions: Class 9 maths ex 1.6 contains a variety of questions with multiple parts, providing ample practice for students.

  5. PDF Availability: Class 9 ex 1.6 solutions are often available in PDF format, allowing students to download and access them offline for convenient studying.

  6. Conceptual Clarity: The ex 1.6 class 9 exercise focuses on reinforcing the understanding of fundamental mathematical concepts related to real numbers and their properties.

  7. Syllabus Alignment: Exercise 1.6 aligns with the prescribed syllabus, covering all relevant topics and concepts.

  8. Free Access: These solutions are typically provided free of charge, ensuring accessibility to all students.

Also see-

NCERT Solutions of Class 10 Subject Wise

Subject Wise NCERT Exemplar Solutions

Frequently Asked Question (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.

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