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 solutions of NCERT 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.
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.
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 CBSE NCERT solutions for class 8 maths chapter 12 exponents and powers. You can get NCERT solutions from class 6 to 12 by clicking on the above link.
Question:(i) Find the multiplicative inverse of the following.
Answer:
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.
Answer:
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.
Answer:
The multiplicative inverse of is
So, the multiplicative inverse of is
Question:(iv) Find the multiplicative inverse of the following.
Answer:
we know,
The multiplicative inverse of is
So, for multiplicative inverse is
Question:(v) Find the multiplicative inverse of the following.
Answer:
The multiplicative inverse of is
So, the multiplicative inverse of is
CBSE 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
Answer:
1025.63 =
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.
Answer:
this is simplified as follows
Question:1(ii) Simplify and write in exponential form.
Answer:
this is simplified as follows
.............
Question:1(iii) Simplify and write in exponential form.
Answer:
this can be simplified as follows
.............
Solutions of NCERT for class 8 maths chapter 12 exponents and powers-Exercise: 12.1
Question:1(i) Evaluate.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
The detailed explanation for the above-written question is as follows,
As we know that
So,
now,
Question:3(ii) Find the value of.
Answer:
The detailed explanation for the above-written question is as follows
Rewrite the equation
.................................
........................
Question:3(iii) Find the value of.
Answer:
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(v) Find the value of.
Answer:
The detailed explanation for the above-written question is as follows
.............. BY using these form of exponential
......... use this
Question:4(i) Evaluate
Answer:
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
Answer:
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
Answer:
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
Answer:
The detailed solution for the above-written question is as follows
.............by using
Question:6(ii) Evaluate
Answer:
The detailed solution for the above-written question is as follows
................ using the form
............using
Question:7(i) Simplify
Answer:
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.
Answer:
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
CBSE 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
Answer:
the standard form of 0.000000564 is
Question:1(ii) Write the following numbers in standard form.
0.0000021
Answer:
The standard form 0.0000021 is
Question:1(iii) Write the following numbers in standard form.
21600000
Answer:
The standard form 21600000 is
Question:1(iv) Write the following numbers in standard form.
15240000
Answer:
The standard form 15240000
Question:2 Write all the facts given in the standard form.
Answer:
Distance between sun and earth
speed of light is
The avg. diameter of red blood cells is
the distance of the moon from the earth is
size of the plant cell is
The diameter of the wire on a computer chip is
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
Answer:
The standard form is
Question:1(ii) Express the following numbers in standard form.
0.00000000000942
Answer:
The standard form is
Question:1(iii) Express the following numbers in standard form.
6020000000000000
Answer:
The standard form is
Question:1(iv) Express the following numbers in standard form.
0.00000000837
Answer:
The standard form of the given number is
Question:1(v) Express the following numbers in standard form.
31860000000
Answer:
The standard form is
Question:3(i) Express the number appearing in the following statements in standard form.
Answer:
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.
Answer:
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.
Answer:
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.
Answer:
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
Answer:
The thickness of a thick paper is 0.07
Answer:
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
Some important result from NCERT solutions for class 8 maths chapter 12 exponents and powers-
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.
Happy Reading!!!