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.

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.

## Access Number Systems Class 9 Chapter 1 Exercise: 1.6

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

Now, on simplifying it we will get

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

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

Now, on simplifying it we will get

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

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

Now, on simplifying it we will get

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

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

Now, on simplifying it we will get

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

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

Now, on simplifying it we will get

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

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

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

Now, on simplifying it we will get

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

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 $\frac{1}{5}$

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 $2^{\frac{13}{15}}$

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 $3^{-21}$

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 $11^{\frac{1}{4}}$

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. 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-

## Subject Wise NCERT Exemplar Solutions

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.

## Upcoming School Exams

#### National Means Cum-Merit Scholarship

Application Date:05 August,2024 - 24 September,2024

#### National Rural Talent Scholarship Examination

Application Date:05 September,2024 - 20 September,2024

#### Meghalaya Board of Secondary School Leaving Certificate Examination

Application Date:05 September,2024 - 23 September,2024

#### Himachal Pradesh Board of Secondary Education 10th Examination

Application Date:09 September,2024 - 14 November,2024

#### Himachal Pradesh Board of Secondary Education 12th Examination

Application Date:09 September,2024 - 14 November,2024

Get answers from students and experts

A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

 Option 1) Option 2) Option 3) Option 4)

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

 Option 1) 2.45×10−3 kg Option 2)  6.45×10−3 kg Option 3)  9.89×10−3 kg Option 4) 12.89×10−3 kg

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

 Option 1) Option 2) Option 3) Option 4)

A particle is projected at 600   to the horizontal with a kinetic energy . The kinetic energy at the highest point

 Option 1) Option 2) Option 3) Option 4)

In the reaction,

 Option 1)   at STP  is produced for every mole   consumed Option 2)   is consumed for ever      produced Option 3) is produced regardless of temperature and pressure for every mole Al that reacts Option 4) at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, will contain 0.25 mole of oxygen atoms?

 Option 1) 0.02 Option 2) 3.125 × 10-2 Option 3) 1.25 × 10-2 Option 4) 2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

 Option 1) decrease twice Option 2) increase two fold Option 3) remain unchanged Option 4) be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

 Option 1) Molality Option 2) Weight fraction of solute Option 3) Fraction of solute present in water Option 4) Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

 Option 1) twice that in 60 g carbon Option 2) 6.023 × 1022 Option 3) half that in 8 g He Option 4) 558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

 Option 1) less than 3 Option 2) more than 3 but less than 6 Option 3) more than 6 but less than 9 Option 4) more than 9