# NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers

**NCERT Solutions for Class 8 Chapter 12 Exponents and Powers** will help students aiming for high marks in their examination. Refer to the NCERT Class 8 Mathematics Exercise Solutions and practise the questions and answers based on the CBSE curriculum to understand the concepts covered in the chapter. We can say that an expression which represents repeated multiplication of the same factor is called a power. For example, in case of 4^{2}, the number 4 is called the base, and the number 2 is the exponent. An Exponent corresponds to the number of times the base is utilized as a factor in an expression.

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## Exercise 12.1 Page No: 197

**1. Evaluate:**

**(i) 3 ^{-2 }(ii) (-4)^{-2 }(iii) (1/2)^{-5} **

**Solution:**

(i) 3^{-2 }= (1/3)^{2}

= 1/9

(ii) **(-4) ^{-2 }= (1/-4)^{2}**

= 1/16

(iii) **(1/2) ^{-5} = (2/1)^{5}**

= 2^{5}

= 32

**2. Simplify and express the result in power notation with positive exponent:**

**(i) (-4) ^{4 }รท(-4)^{8} **

**(ii) (1/2 ^{3})^{2} **

**(iii) -(3) ^{4}ร(5/3)^{4} **

**(iv) (3 ^{-7}รท3^{-10})ร3^{-5} **

**(v) 2 ^{-3}ร(-7)^{-3}**

**Solution:**

(i)

= (-4)^{5}/(-4)^{8}

= (-4)^{5-8}

= 1/(-4)^{3}

(ii) **(1/2 ^{3})^{2} **

= 1^{2}/(2^{3})^{2}

= 1/2^{3ร2} = 1/2^{6}

(iii) **-(3) ^{4}ร(5/3)^{4} **

= (-1)^{4}ร3^{4}ร(5^{4}/3^{4} )

= 3^{(4-4)}ร5^{4}

= 3^{0}ร5^{4} = 5^{4}

(iv)** **

= (3^{-7}/3^{-10})ร 3^{-5}

= 3^{-7 โ (-10) }ร 3^{-5}

= 3^{(-7+10)}ร3^{-5}

= 3^{3}ร3^{-5}

= 3^{(3+-5)}

= 3^{-2}

=1/3^{2}

(v) 2^{-3}ร(-7)^{ โ 3}

= (2ร-7)^{-3}

(Because a^{m}รb^{m} = (ab)^{m})

= 1/(2ร-7)^{3}

= 1/(-14)^{3}

**3. Find the value of :**

**(i) (3 ^{0}+4^{-1})ร2^{2}**

**(ii) (2 ^{-1}ร4^{-1})รท2^{ โ 2}**

**(iii) (1/2) ^{-2}+(1/3)^{-2}+(1/4)^{-2}**

**(iv) (3 ^{-1}+4^{-1}+5^{-1})^{0}**

**(v) {(-2/3) ^{-2}}^{2}**

**Solution:**

(i)(3^{0}+4^{โ 1})ร2^{2} = (1+(1/4))ร2^{2}

= ((4+1)/4 )ร2^{2}

= (5/4)ร2^{2}

= (5/2^{2})ร2^{2}

= 5ร2^{(2-2)}

= 5ร2^{0}

= 5ร1 = 5

(ii)(2^{-1}ร4^{-1})รท2^{-2}

= [(1/2)ร(1/4)] รท(1/4)

= (1/2ร1/2^{2} )รท 1/4

= 1/2^{3}รท1/4

= (1/8)ร(4)

= 1/2

(iii) **(1/2) ^{-2}+(1/3)^{-2}+(1/4)^{-2}**

= (2^{-1})^{-2}+(3^{-1})^{-2}+(4^{-1})^{-2}

= 2^{(-1ร-2)}+3^{(-1ร-2)}+4^{(-1ร-2)}

= 2^{2}+3^{2}+4^{2}

= 4+9+16

=29

(iv) (3^{-1}+4^{-1}+5^{-1})^{0}

= 1

(v) **{(-2/3) ^{-2}}^{2} = (-2/3)^{-2ร2}**

= (-2/3)^{-4}

= (-3/2)^{4}

= 81/16

**4. Evaluate**

**(i) (8 ^{-1}ร5^{3})/2^{-4}**

**(ii) (5 ^{-1}ร2^{-2})ร6^{-1} **

**Solution:**

(i) (8^{-1}ร5^{3})/2^{-4}

=

= 2ร125 = 250

**(ii)** **(5 ^{-1}ร2^{-2})ร6^{-1} **

= (1/10)ร1/6

= 1/60

**5. Find the value of m for which 5^{m }รท 5^{-3} = 5^{5}**

**Solution:**

5* ^{m}* รท 5

^{-3}= 5

^{5}

5^{(m-(-3) )} = 5^{5}

5^{m+3} =5^{5}

Comparing exponents both sides, we get

m+3 = 5

m = 5-3

m = 2

**6. Evaluate**

**(i) **

**(ii) **

**Solution:**

**(i)**

= 3-4

= -1

**(ii)**

=

=

=

= 512/125

**7. Simplify.**

**(i) **

**(ii) **

Solution:

**(i)**

=

=

**(ii)**

=

=

=

=

= 1ร1ร3125

= 3125

## Exercise 12.2 Page No: 200

**1. Express the following numbers in standard form.**

**(i) 0.0000000000085**

**(ii) 0.00000000000942**

**(iii) 6020000000000000**

**(iv) 0.00000000837**

**(v) 31860000000**

**Solution:**

(i) 0.0000000000085 = 0.0000000000085ร(10^{12}/10^{12}) = 8.5 ร10^{-12}

(ii) 0.00000000000942 = 0.00000000000942ร(10^{12}/10^{12}) = 9.42ร10^{-12}

(iii) 6020000000000000 = 6020000000000000ร(10^{15}/10^{15}) = 6.02ร10^{15}

(iv) 0.00000000837 = 0.00000000837ร(10^{9}/10^{9}) = 8.37ร10^{-9}

(v) 31860000000 = 31860000000ร(10^{10}/10^{10}) = 3.186ร10^{10}

**2.Express the following numbers in usual form.**

**(i) 3.02ร10 ^{-6}**

**(ii) 4.5ร10 ^{4}**

**(iii)3ร10 ^{-8}**

**(iv)1.0001ร10 ^{9}**

**(v) 5.8ร10 ^{12}**

**(vi)3.61492ร10 ^{6}**

Solution:

(i) 3.02**ร**10^{-6} = 3.02/10^{6} = 0 .00000302

(ii) 4.5**ร**10^{4} = 4.5**ร**10000 = 45000

(iii) 3**ร**10^{-8} = 3/10^{8} = 0.00000003

(iv) 1.0001**ร**10^{9} = 1000100000

(v) 5.8**ร**10^{12} = 5.8**ร**1000000000000 = 5800000000000

(vi) 3.61492**ร**10^{6 }= 3.61492**ร**1000000 = 3614920

**3. Express the number appearing in the following statements in standard form.**

**(i) 1 micron is equal to 1/1000000 m.(ii) Charge of an electron is 0.000, 000, 000, 000, 000, 000, 16 coulomb.(iii) Size of bacteria is 0.0000005 m(iv) Size of a plant cell is 0.00001275 m(v) Thickness of a thick paper is 0.07 mm**

**Solution :**

(i) 1 micron = 1/1000000

= 1/10^{6}

= 1ร10^{-6}

(ii) Charge of an electron is 0.00000000000000000016 coulombs.

= 0.00000000000000000016**ร**10^{19}/10^{19}

= 1.6**ร**10^{-19 }coulomb

(iii) Size of bacteria = 0.0000005

= 5/10000000 = 5/10^{7} = 5ร10^{-7} m

(iv) Size of a plant cell is 0.00001275 m

= 0.00001275ร10^{5}/10^{5}

= 1.275ร10^{-5}m

(v) Thickness of a thick paper = 0.07 mm

0.07 mm = 7/100 mm = 7/10^{2} = 7ร10^{-2} mm

**4. In a stack there are 5 books each of thickness 20 mm and 5 paper sheets each of thickness 0.016 mm. What is the total thickness of the stack?**

Solution:

Thickness of one book = 20 mm

Thickness of 5 books = 20ร5 = 100 mm

Thickness of one paper = 0.016 mm

Thickness of 5 papers = 0.016ร5 = 0.08 mm

Total thickness of a stack = 100+0.08 = 100.08 mm

= 100.08ร10^{2}/10^{2} mm

mm

### NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers

These NCERT solutions help students to gain a better understanding of the topic and learn the concepts with ease. This learning material is designed by subject experts as per the CBSE latest syllabus prescribed by the board. In Class 8 CBSE chapter 12 of Maths, students will learn about how to write large numbers more conveniently using exponents and powers, express numbers in standard form, dealing with negative exponents, various laws of exponents and many more.**NCERT Solutions For Class 8 Maths Chapter 12 Exercises:**

Get detailed solution for all the questions listed under below exercises:

Exercise 12.1 Solutions : 7 Questions (Short answers)

Exercise 12.2 Solutions : 4 Questions (Short answers)

### NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers

NCERT Solutions for Class 8 Maths Chapter 12, Exponents and Powers is about the law of exponents, powers and their applications.**The main topics covered in this chapter include:**

Exercise | Topic |

12.1 | Introduction |

12.2 | Powers with Negative Exponents |

12.3 | Laws of Exponents |

12.4 | Use of Exponents to Express Small Numbers in Standard Form |

### Key Features of NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers

- Easy and simple language used.
- NCERT Solutions will help in boosting the confidence level among students.
- Subject experts have consolidated all exercises questions at one place which could feature in your exam.
- All solutions are structured in an easy and logical language for quick revisions.
- NCERT Solutions are helpful for preparation of competitive exams.

## Frequently Asked Questions on NCERT Solutions for Class 8 Maths Chapter 12

### Does NCERT Solutions for Class 8 Maths Chapter 12 help you to clear board exams?

Yes, NCERT Solutions for Class 8 Maths Chapter 12 is one of the important chapters of Class 8 Maths of NCERT Solutions. These solutions are focused on learning various Mathematics tricks and shortcuts for quick and easy calculations. This makes them learn and clear the Maths subject in board exams.

### How NCERT Solutions for Class 8 Maths Chapter 12 helps in learning exponents and powers?

NCERT Solutions for Class 8 Maths Chapter 12 is created by our faculty in an interactive manner to make it easy for the students to understand the concepts. Students can refer to the PDF of solutions as a major study material to improve their speed in solving problems accurately.

### How many questions present in NCERT Solutions for Class 8 Maths Chapter 12 ?

12th Chapter of NCERT Solutions for Class 8 Maths has 2 exercises. In that first exercise contains 7 questions and the last or second exercise has 4 questions. So there are a total of 11 short answer questions that are present in NCERT Solutions for Class 8 Maths Chapter 12.