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

NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers will remove all your queries concerning the Chapter. In this chapter of NCERT Solutions, you will learn about the concept of Exponents and Powers using numerous examples and illustrations. Further, the chapter sheds light on various concepts viz. powers with negative exponents, the different laws of exponents, use of exponents to express the numbers in standard form and comparison of extremely large numbers with the small numbers.

CBSE NCERT Class 8 Maths Chapter 12 has only 2 exercises with a total of 11 questions. Most of the questions have sub-parts so you have enough questions to practice. These exercises will help you to fathom all the concepts and so does boost your confidence level with Mathematics. The level of the questions contained in this chapter is basic as well as advanced. This solution will help you to comprehend the right methodology to be followed to solve the questions. As anything in the exams can be asked so it is extremely imperative to solve a variety of questions.

Exercise-wise solutions for NCERT Class 8 Maths Chapter 12 are provided by us. Our team has solved all your doubts with proper reasoning. Answers to every NCERT textbook question are provided in a step by step manner. This sagaciously designed material by the dedicated experts presents even the mayhem Mathematical concepts into an entirely intelligible solution to enjoy.

## Important Topics of NCERT Solutions for Class 8 Maths Chapter 12 – Exponents and Powers

Do you know the mass of the Planet Earth? The Mass of Earth is 5,970,000,000,000,000,000,000,000 kg. We can simply write large numbers using the exponents 5.97 x 10^{24} kg. Here 10 is the base and 24 is an exponent. So, we will say 10 raised to the power 24.

**Powers with Negative Exponents**

10^{2} = 10 x 10 =100. Here, the exponent is a positive integer.

10^{-1} =?

Here, the exponent is a negative integer. So, the exponent is decreased by 1 and hence, the value becomes one-tenth of the original value.

We will say 10^{-1} = 1/10.

10^{-2} = 1/10^{2} or we can write it as 10^{2} = 1/10^{-2}

3^{-2} = 1/3^{2} or we can write it as 3^{2} = 1/3^{-2}

Any non-zero integer, say a^{-m} = 1/a^{m} and where m is a positive integer. So, a^{-m} is the multiplicative inverse of the value a^{m}.

To write any number in an expanded form using exponents, we can follow the given example:

1425.36 = 1 x 1000 + 4 x 100 + 2 x 10 + 5 x 1 + 3/10 + 6/100

= 1 x 10^{3} + 4 x 10^{2} + 2 x 10 + 5 x 1 +3 x 10^{-1} + 6 x 10^{-2}

**Laws of Exponents**

Where there is any non-zero integer like a, am x an = am + n, m and n are natural numbers. Where the base value is the same and they are multiplied, then the exponents will be added.

**For example:**

2^{-3} = 1/23 and 2^{-2} = 1/2^{2}

So, 2^{-3} x 2^{-2} = 1/ 2^{3} x 1/ 2^{2}

= 1/ 2^{3} x 2^{2}

= 1/ 2^{3+2}

= 2^{-5}

Following are the various Laws of Exponents:

Here, a and b are non-zero integers. M and N are any integers.

- a
^{m}/ a^{n}= a^{m-n} - (a
^{m})^{n}= a^{mn} - a
^{m}x b^{m}= (ab)^{m} - a
^{m}/ b^{m}= (a / b)^{m} - a
^{0}= 1

Let us now solve some examples using the above laws:

~ To simplify 2^{5} ÷ 2^{-6}

We will apply this law: a^{m} / a^{n} = a^{m-n}

So, it will become 2^{5-(-6)} = 2^{11}

~ To express 4^{-3} as a power and with the base value of 2, we will simply use (am)^{n} = a^{mn}

4 = 2 x 2 = 2^{2}

So, 4^{-3} = (2 x 2)^{-3}

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

=2^{2x (-3)}

= 2^{-6}

~ To find out the value of (2/3)^{-2}, use the following simple steps:

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

Apply (a / b)^{-m} = (b / a)^{m}

= 3^{2} / 2^{2}

= 9 / 4

**Use of Exponents to Express Small Numbers in the Standard Form**

We can express very large numbers like 150,000,000,000 into Standard Form as 1.5 x 10^{11}. Here, the decimal is shifted to 11 places to the left side. Similarly, we can express a very small number into Standard Form.

**For example** 0.000007 m

= 7 / 1000000. Here, the decimal is moved 6 places to the right side. 7/10^{6} = 7 x 10^{-6}. So, we can say 0.000007 m = 7 x 10^{-6} m.

**Comparing Very Large and Very Small Numbers**

While comparing very large numbers with small numbers, first we have to convert the given numbers into the Standard Form and thereafter we will simplify them. Below is an example of this:

Compare the size of a Red Blood Cell with that of a Plant Cell. The size of the Red Blood Cell is 0.000007 m and the size of a Plant Cell is 0.00001275 m. First, we will convert these values into a Standard Form.

0.000007m = 7 x 10^{-6} m

0.00001275 = 1.275 x 10^{-5} m

After converting into Standard Form, we will now go on to solve them.

7 x 10^{-6} / 1.275 x 10^{-5}

= 7 x 10^{-6-(-5)} / 1.275

= 7 x 10^{-1} / 1.275

= 0.7 / 1.275

=0.7 / 1.3

= 1/2 (approx.)

After solving it, we can say that the Red Blood Cell is half in the size as compared to that of the Plant Cell.

## Discussion of Exercise of NCERT Class 8 Maths Chapter 12

The NCERT Class 8 Maths Chapter 12 consists of 2 exercises- 12.1 and 12.2. Now, let us discuss each of them-

**Exercise 12.1-**

- In the first question, you have to evaluate the given numbers.
- The second question is about simplifying the given values and then expressing the result into power notation with a positive exponent.
- You have to find the value of the given numbers in question third.
- In the fourth and the sixth question, you have to evaluate the given numbers.
- In the fifth question, you have to find the value of the missing number.
- Lastly, in the seventh question, the given numbers are to be written in a simplified manner.

**Exercise 12.2- **

- In the first question, you have to write the given numbers in standard form.
- You have to express the given numbers in the usual form in the second question.
- The third question is about writing the standard form of the numbers given in the statements.
- You have to calculate the total thickness of the stack in the fourth question.

## Benefits of using NCERT Solutions for Class 8 Mathematics Chapter 12 by Instasolv

The NCERT Solutions for Class 8 Maths Chapter 12 is a concise compilation covering various facts and concepts which have been thoroughly explained with numerous examples. These crisp and to the point solutions will help you in building a very strong foundation of maths. Meticulously prepared according to the latest CBSE syllabus, this solution will help you to revise each topic very quickly.

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