NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers

NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers - If someone asks you about the mass of your bag? Probably your answer is 7 kg but what if someone asks you about the mass of the earth. Mass of the earth is 5,970,000,000,000,000,000,000, 000 kg,(no need to remember) which is a very big data. You can write such large numbers more conveniently using exponents. In this article, you will get NCERT solutions for Class 8 Maths chapter 12 Exponents and Powers explained in a detailed manner to get a better understanding of the chapter. In this chapter, you will learn how to make the representation of bigger numbers easier using about exponents and powers. This is a new concept but if you go through NCERT solutions for Class 8 Maths chapter 12 Exponents and Powers, you will understand it completely. Let’s look at a scenario from our daily life to understand this chapter.

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Example-

 Questions Assume it’s your answer Distance between your home and school 15 KM Distance between Bangalore and Delhi 1500 KM Distance between India and South America 15000 KM Distance between Earth and the Sun 150000000 KM

In the above example, you can see that a very big number like 150000000 KM is difficult to understand and becomes more complex or tough to understand, read and operate. So it can be represented in exponent form as 1.5x10 8 km. The exponent of a number, describe that for how many times a number(base) will be multiplied. The base is the number that is going to be multiplied.

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Example- , where 6 is the base and 3 is the power. Multiplying three sixes together gives 6*6*6 = 216.

There are 11 questions in 2 exercises of the textbook. All these questions are explained in NCERT solutions for Class 8 Maths chapter 12 Exponents and Powers. You can get NCERT Solutions from Classes 6 to 12 by clicking on the above link. Here you will get the detailed NCERT Solutions for Class 8 by clicking on the link.

NCERT Solutions for Class 8 Maths Chapter 12 Topic 12.2 Powers With Negative Exponents

Question:(i) Find the multiplicative inverse of the following.

The detailed explanation for the question is written below,

The multiplicative inverse is

So, the multiplicative inverse of is

Question:(ii) Find the multiplicative inverse of the following.

Here is the detailed solution for the above question,

As we know,

The multiplicative inverse of is

So, the multiplicative inverse of is

Question:(iii) Find the multiplicative inverse of the following.

The multiplicative inverse of is

So, the multiplicative inverse of is

Question:(iv) Find the multiplicative inverse of the following.

we know,

The multiplicative inverse of is

So, for multiplicative inverse is

Question:(v) Find the multiplicative inverse of the following.

The multiplicative inverse of is

So, the multiplicative inverse of is

NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Topic 12.2 Powers With Negative Exponents

Question:(i) Expand the following numbers using exponents.

1025.63

1025.63 =

Question:(ii) Expand the following numbers using exponents.

1256.249

1256.249

NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Topic 12.3 Laws Of Exponents

Question:1(i) Simplify and write in exponential form.

this is simplified as follows

Question:1(ii) Simplify and write in exponential form .

this is simplified as follows

.............

Question:1(iii) Simplify and write in exponential form.

this can be simplified as follows

.............

NCERT Solutions for Class 8 Maths Chapter 12 Exponents And Powers-Exercise: 12.1

Question:1 (i) Evaluate.

The detailed explanation for the above-written question is as follows,

We know that,

So, here m =2 and a = 3

Question: 1(ii) Evaluate.

The detailed explanation for the above-written question is as follows

We know that,

So, here (a = -4) and (m = 2)

Then according to the law of exponent

[ negative negative = positive]

Question: 1(iii) Evaluate.

The detailed solution for the above-written question is as follows

We know that,

So, here

a = 1 and b = 2 and m =-5

According to the law of exponent

Question: 2(i) Simplify and express the result in power notation with a positive exponent.

The detailed solution for the above-written question is as follows

We know the exponential formula

and

So according to this

a = -4, m = 5 and n = 8

Question: 2(ii) Simplify and express the result in power notation with positive exponent.

The detailed solution for the above-written question is as follows

We know the exponential formula

and and

So, we have given

a = 1, b=2

By using above exponential law,

Question: 2(iii) Simplify and express the result in power notation with a positive exponent.

The detailed solution for the above-written question is as follows,

We know the exponential formula

So,

Question: 2(iv) Simplify and express the result in power notation with a positive exponent.

The detailed explanation for the above-written question is as follows

As we know the exponential form

By using these two form we get,

Question:2(v) Simplify and express the result in power notation with positive exponent.

The detailed solution for the above-written question is as follows,

we know the exponential forms

&

So, according to our data,

here initially we use first forms and then the second one.

Question:3(i) Find the value of.

The detailed explanation for the above-written question is as follows,

As we know that

So,

now,

Question: 3(ii) Find the value of.

The detailed explanation for the above-written question is as follows

Rewrite the equation

.................................

........................

Question: 3(iii) Find the value of.

The detailed explanation for the above-written question is as follows,

This is the exponential form

So,

.......................using this form

= 4+9+16

= 29

Question: 3(iv) Find the value of.

since we know that

Question: 3(v) Find the value of.

The detailed explanation for the above-written question is as follows

.............. BY using these form of exponential

......... use this

Question:4(i) Evaluate

The detailed explanation for the above written question is as follows

after rewriting the above equation we get,

...........as we know that

An alternate method,

here you can use first and after that use

Question: 4(ii) Evaluate

The detailed explanation for the above-written question is as follows

We clearly see that this is in the form of

So,

Question: 5 Find the value of for which

We have,

Here a = 5 and n =-3 and m-n = 5

therefore,

By comparing from both sides we get

m+3 = 5

m= 2

Question: 6(i) Evaluate

The detailed solution for the above-written question is as follows

.............by using

Question: 6(ii) Evaluate

The detailed solution for the above-written question is as follows

................ using the form

............using

Question: 7(i) Simplify

The detailed solution for the above-written question is as follows

we can write

So, after rewriting the equation,

.................using the form

.............(By expanding we have now)

Question: 7(ii) Simplify.

The detailed solution for the above-written question is

we can write 125 = and can be written as

Now, rewriting the equation, we get

.............by using

.....................Use

.........................As . can be cancelled out with the denominator

NCERT Solutions for Class 8 Maths Chapter 12 Exponents and Powers Topic 12.4 Use Of Exponents To Express Small Numbers In Standard Form

Question: 1(i) Write the following numbers in standard form.

0.000000564

the standard form of 0.000000564 is

Question: 1(ii) Write the following numbers in standard form.

0.0000021

The standard form 0.0000021 is

Question: 1(iii) Write the following numbers in standard form.

21600000

The standard form 21600000 is

Question: 1(iv) Write the following numbers in standard form.

15240000

The standard form 15240000

Question: 2 Write all the facts given in the standard form .

1. Distance between sun and earth

2. speed of light is

3. The avg. diameter of red blood cells is

4. the distance of the moon from the earth is

5. size of the plant cell is

6. The diameter of the wire on a computer chip is

7. the height of the Mount Everest is

NCERT Solutions for Class 8 Maths Chapter 12 Exponents And Powers-Exercise: 12.2

Question: 1(i) Express the following numbers in standard form .

0.0000000000085

The standard form is

Question: 1(ii) Express the following numbers in standard form.

0.00000000000942

The standard form is

Question: 1(iii) Express the following numbers in standard form.

6020000000000000

The standard form is

Question: 1(iv) Express the following numbers in standard form.

0.00000000837

The standard form of the given number is

Question: 1(v) Express the following numbers in standard form.

31860000000

The standard form is

Question: 2(i) Express the following numbers in usual form.

this is the usual form

Question: 2(ii) Express the following numbers in usual form.

this is the usual form

Question:2(iii) Express the following numbers in the usual form.

this is the usual form

Question: 2(iv) Express the following numbers in usual form.

this is the usual form

Question: 2(v) Express the following numbers in usual form.

this is the usual form

Question:2(vi) Express the following numbers in usual form.

17155

Question:3(i) Express the number appearing in the following statements in standard form.

1 micron is equal to .

1 micron is equal to

Question:3(ii) Express the number appearing in the following statements in standard form.

Charge of an electron is 0.000,000,000,000,000,000,16 coulomb.

Charge of an electron is 0.000,000,000,000,000,000,16 coulomb.

coulomb.

Question:3(iii) Express the number appearing in the following statements in standard form.

Size of a bacteria is 0.0000005 m.

Size of a bacteria is 0.0000005 m

Question:3(iv) Express the number appearing in the following statements in standard form.

Size of a plant cell is 0.00001275 m.

Size of a plant cell is0.00001275m

Question:3(v) Express the number appearing in the following statements in standard form.

Thickness of a thick paper is 0.07 mm

The thickness of a thick paper is 0.07

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

the thickness of each book = 20mm

So, the thickness of 5 books =

the thickness of one paper sheet =0.016mm

So, the thickness of 5 paper sheet =

the total thickness of the stack = (100+0.08)mm

=100.08 mm or

Exponents and Powers Class 8 Math Chapter 12-Topics

• Powers with Negative Exponents
• Laws of Exponents
• Use of Exponents to Express Small Numbers in Standard Form
• Comparing very large and very small numbers

NCERT Solutions for Class 8 Maths: Chapter-Wise

 Chapter -1 Rational Numbers Chapter -2 Linear Equations in One Variable Chapter-3 Understanding Quadrilaterals Chapter-4 Practical Geometry Chapter-5 Data Handling Chapter-6 Squares and Square Roots Chapter-7 Cubes and Cube Roots Chapter-8 Comparing Quantities Chapter-9 Algebraic Expressions and Identities Chapter-10 Visualizing Solid Shapes Chapter-11 Mensuration Chapter-12 Exponents and Powers Chapter-13 Direct and Inverse Proportions Chapter-14 Factorization Chapter-15 Introduction to Graphs Chapter-16 Playing with Numbers

NCERT Solutions for Class 8: Subject-Wise

• NCERT Solutions for Class 8 Maths
• NCERT Solutions for Class 8 Science

Some Important Results From NCERT Solutions for Class 8 Maths Chapter 12 Exponents And Powers-

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The above results are valid for both positive and negative powers. You don't have to remember the results. If you understood the concepts you can derive all the above results. You can go through NCERT solutions for class 8 maths chapter 12 exponents and powers to get conceptual clarity.