# NCERT Solutions for Class 9 Maths Chapter 1 Number Systems (Ex 1.6) Exercise 1.6

Mathematics is an important subject for students in Class 9. Students’ capacity to reason and think logically necessitates a firm grasp of the fundamental themes of mathematics. With an understanding of mathematical concepts, students may learn to solve problems that have relevance to fields in the actual world. Every subject involves the application of Mathematics in some manner. With the use of its principles, students can pursue further education and research in diverse fields such as Astronomy, Astrophysics, Statistics, Weather Forecasting, and others. One of the basic disciplines of the academic curriculum, Mathematics is studied in schools beginning in the first grade. The foundational concepts of Mathematics are important for a student’s general growth.

NCERT textbooks are thorough and all-inclusive in their own right, and the academic curriculum of the CBSE is closely centred around the content of the NCERT textbooks. Students ought to read and study these books in depth. While it is highly recommended that students should broaden their conceptual horizons by referring to a variety of reference materials, it is imperative for them to study every single topic from the NCERT books. It is important to properly understand the NCERT textbooks before reading any other books.

## Access NCERT Solutions for Class 9 Maths Chapter 1 – Number System

All the tools required for competitive test preparation are available on the Extramarks website and mobile application. Students may utilise the learning assets provided by the Extramarks learning portal to prepare for a variety of competitive examinations, including JEE Mains, NEET, JEE Advance, CUET, and others. The solutions to every chapter and topic are accessible on Extramarks. Students may visit the Extramarks website and obtain the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.6 in PDF format for further assistance with the designated chapter. The NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.6, can help students focus on the curriculum of Class 9 Mathematics in order to ace exams with ease. To score well on the Class 9 examinations, students must adequately engage with the entire Class 9 syllabus. A student’s academic future is greatly influenced by the grades they earn in Class 9, as it boosts the confidence. To begin, they must be completely focused.

## NCERT Solutions for Class 9 Maths Chapter 1 Number System

Students can find the NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.6 on the Extramarks website and mobile app. Students’ confidence with regard to the Mathematics examination is increased by using the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.6. The NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.6 may be used by students to enhance the quality of Mathematics examination preparation. With the aid of the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.6, students may quickly review key ideas and formulae. Students of the Central Board of Secondary Education may learn the correct way to respond to various kinds of questions with the help of NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.6. The NCERT books are the basic books for understanding complex concepts in Mathematics without any hindrance. Hence, students are advised to follow the NCERT books solely to acquire proficiency in the mathematics curriculum in the senior classes as well.

### NCERT Solutions for Class 9 Maths

The links provided further below on this page allow students to obtain PDFs of the chapter-by-chapter solutions to these issues. Students can also download NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.6. Extramarks strives to provide students with the best possible learning experience. Hence, NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.6, are accurate and precise. The prescribed Mathematics textbook of for Class 9 consists of 15 chapters.

• Chapter 1 Number System
• Chapter 2 Polynomials
• Chapter 3 Coordinate Geometry
• Chapter 4 Linear Equations in Two Variables
• Chapter 5 Introduction to Euclid Geometry
• Chapter 6 Lines and Angles
• Chapter 7 Triangles
• Chapter 9 Areas of Parallelograms and Triangles
• Chapter 10 Circles
• Chapter 11 Constructions
• Chapter 12 Heron’s Formula
• Chapter 13 Surface Areas and Volumes
• Chapter 14 Statistics
• Chapter 15 Probability

### Access Other Exercise Solutions of Class 9 Maths Chapter 1 – Number Systems

As “Number System” is one of the most important chapters of Class 9 Mathematics, students must solve every exercise of the given chapter. Extramarks has provided comprehensive solutions to each exercise in Chapter 1- Number System. The first exercise, 1.1, has a total of 4 questions, and all of them are short answer type questions. The second exercise, 1.2, has a total of 4 questions, and every question is of the short answer type. Further third exercise 1.3 has a total of 9 questions, of which 8 are short answer types and one is a long answer. The fourth 1.4 exercise has a total of 2 questions, and both of the questions are long answer types. The fifth exercise 1.5 has a total number of 5 questions in which 4 questions are short answer type and 1 question is a long answer type. The solutions for all these exercises can be procured from the Extramarks digital learning portal. Finally, the sixth exercise has a total number of 3 questions and all of them are short answer type. Credible solutions for the same can be acquired in the form of NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.6. Exercise 1.6 Class 9 Maths is an easy exercise so students must ensure to practice it on a regular basis. Exercise 1.6 Class 9 Maths Solutions, is key reference material for students who are facing conceptual challenges while solving questions.

### NCERT Solutions for Class 9

Students can also access a variety of learning assets along with the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.6. Quality reference material for every academic discipline is available on the Extramarks website and mobile application. Therefore, students are advised to visit the Extramarks website and find any material that would be helpful for them. Students can also access the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.6, on the Extramarks learning platform. They can find notes, important questions, and exemplar solutions for the chapter titled “Number System.” Students can also access past years’ papers and efficiently solve them with help of  NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.6.

### CBSE Study Materials for Class 9

It is noteworthy that Class 9 Maths Chapter 1 Exercise 1.6 Solutions are designed by subject matter experts of Mathematics with accuracy and precision so that students would not have to face any issues while solving questions. Students can easily access the NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.6, at their convenience. Students can access reference materials for the academic curriculum of diverse subjects that are part of the prescribed curriculum for Class 9, including Mathematics, Science, English, Hindi, etc.

### CBSE Study Materials

It is important for students who follow the CBSE board curriculum to be aware that while they are able to pass the CBSE examinations by studying only the NCERT texts, this can be occasionally challenging. It can sometimes be challenging for students to solve questions from the NCERT Mathematics book. Extramarks has adhered to the CBSE guidelines in the process of preparing NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.6. The chapters in NCERT textbooks are accompanied by a number of challenging assessments referred to as exercises. Accordingly, students must know that study materials for the curriculum of the CBSE Board are available on Extramarks, and from there, students can also download NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.6. They will be able to solve any question of Class 9 Maths Chapter 1 Exercise 1.6 with the help in NCERT Solutions For Class 9 Maths Chapter 1 Exercise 1.6.

Q.1

$\mathrm{Find}:\text{ }\left(\text{i}\right){64}^{\frac{1}{2}}\text{ }\left(\mathrm{ii}\right){32}^{\frac{1}{5}}\text{ }\left(\mathrm{iii}\right){125}^{\frac{1}{3}}$

Ans

$\begin{array}{l}\left(\mathrm{i}\right)\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}{64}^{\frac{1}{2}}={\left({2}^{6}\right)}^{\frac{1}{2}}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}={2}^{6×\frac{1}{2}}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}={2}^{3}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=8\\ \left(\mathrm{ii}\right)\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}{32}^{\frac{1}{5}}={\left({2}^{5}\right)}^{\frac{1}{5}}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}={2}^{5×\frac{1}{5}}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}={2}^{1}\text{\hspace{0.17em}}=2\\ \left(\mathrm{iii}\right)\text{\hspace{0.17em}\hspace{0.17em}}{125}^{\frac{1}{3}}={\left({5}^{3}\right)}^{\frac{1}{3}}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}={5}^{3×\frac{1}{3}}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}={5}^{1}\text{\hspace{0.17em}}=5\end{array}$

Q.2

$\text{Find: }\left(\text{i}\right){\text{9}}^{\frac{\text{3}}{\text{2}}}\text{ }\left(\text{ii}\right){\text{32}}^{\frac{\text{2}}{\text{5}}}\text{ }\left(\text{iii}\right){\text{16}}^{\frac{\text{3}}{\text{4}}}\text{ }\left(\text{iv}\right){\text{125}}^{\frac{-\text{1}}{\text{3}}}$

Ans

$\begin{array}{l}\left(\mathrm{i}\right)\text{\hspace{0.17em}\hspace{0.17em}}{9}^{\frac{3}{2}}={\left({3}^{2}\right)}^{\frac{3}{2}}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}={3}^{2×\frac{3}{2}}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}={3}^{3}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=27\\ \left(\mathrm{ii}\right)\text{\hspace{0.17em}}{32}^{\frac{2}{5}}={\left({2}^{5}\right)}^{\frac{2}{5}}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}={{2}^{5×}}^{\frac{2}{5}}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}={2}^{2}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=4\\ \left(\mathrm{iii}\right)\text{\hspace{0.17em}}{16}^{\frac{3}{4}}={\left({2}^{4}\right)}^{\frac{3}{4}}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}={2}^{4×\frac{3}{4}}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}={2}^{3}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=8\\ \left(\mathrm{iv}\right)\text{\hspace{0.17em}}{125}^{\frac{-1}{3}}={\left({5}^{3}\right)}^{\frac{-1}{3}}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}={{5}^{3×}}^{\frac{-1}{3}}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}={5}^{-1}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\frac{1}{5}\end{array}$

Q.3

$\mathrm{Simplify}:\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left(\mathrm{i}\right)\text{\hspace{0.17em}}{2}^{\frac{2}{3}}.{2}^{\frac{1}{5}}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left(\mathrm{ii}\right)\text{\hspace{0.17em}}{\left(\frac{1}{{3}^{3}}\right)}^{7}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left(\mathrm{iii}\right)\text{\hspace{0.17em}}\frac{{11}^{\frac{1}{2}}}{{11}^{\frac{1}{4}}}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left(\mathrm{iv}\right){7}^{\frac{1}{2}}.{8}^{\frac{1}{2}}$

Ans

$\begin{array}{l}\left(\mathrm{i}\right)\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}{2}^{\frac{2}{3}}.{2}^{\frac{1}{5}}={2}^{\frac{2}{3}+\frac{1}{5}}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left[\because {\mathrm{x}}^{\mathrm{a}}.{\mathrm{x}}^{\mathrm{b}}={\mathrm{x}}^{\mathrm{a}+\mathrm{b}}\right]\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}={2}^{\frac{10+3}{15}}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}={2}^{\frac{13}{15}}\\ \\ \left(\mathrm{ii}\right)\text{\hspace{0.17em}}{\left(\frac{1}{{3}^{3}}\right)}^{7}=\frac{1}{{3}^{3×7}}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}=\frac{1}{{3}^{21}}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}={3}^{-21}\\ \left(\mathrm{iii}\right)\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\frac{{11}^{\frac{1}{2}}}{{11}^{\frac{1}{4}}}={11}^{\frac{1}{2}-\frac{1}{4}}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left[\because \frac{{\mathrm{x}}^{\mathrm{a}}}{{\mathrm{x}}^{\mathrm{b}}}={\mathrm{x}}^{\mathrm{a}-\mathrm{b}}\right]\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}={11}^{\frac{2-1}{4}}\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}={11}^{\frac{1}{4}}\\ \\ \left(\mathrm{iv}\right)\text{\hspace{0.17em}}{7}^{\frac{1}{2}}.{8}^{\frac{1}{2}}={\left(7×8\right)}^{\frac{1}{2}}\text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}\left[\because {\mathrm{x}}^{\mathrm{m}}.{\mathrm{y}}^{\mathrm{m}}={\left(\mathrm{xy}\right)}^{\mathrm{m}}\right]\\ \text{\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}}={56}^{\frac{1}{2}}\end{array}$