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In this modern world with higher-level mathematics, finding the area of squares, calculating the compound interest or expressing larger data, nothing is possible without Exponents and Powers. This chapter on Exponents and Powers helps represent and work with larger numbers and calculations. This chapter lays the introduction to the rules and properties of exponents. None of the higher mathematical topics can be covered without this concept of Exponents and Powers. The NCERT Solutions for Class 8 Maths provide students with comprehensive step-by-step solutions to every exercise problem. These step-by-step solutions help students understand and apply the concepts effectively.
These NCERT Solutions are highly reliable as they are developed by the subject matter experts of Careers360. These solutions are of great help for the exam preparation as the students can practice the exercise problems and check the answers to evaluate their performance, and can focus on their weaker areas. Students can refer to the NCERT Solutions for Class 8 to access the subject-wise solutions for the Class.
Students who wish to access the NCERT solutions for Class 8 Maths Chapter 10, Exponents and Powers, can click on the link below to download the entire solutions in PDF format for free.
NCERT Solutions for Class 8 Maths Chapter 10 Exponents and Powers Exercise 10.1 Page Number: 125-126 Number of Questions: 7 |
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
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
So according to this
a = -4, m = 5 and n = 8
Question: 2(ii) 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, we have given
a = 1, b=2
By using the 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 forms, we get,
Question:2(v) 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 forms
So, according to our data,
Here, initially, we use the first form 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,
= 4+9+16
= 29
Question: 3(iv) Find the value of.
Answer:
since we know that
Question: 3(v) Find the value of.
Answer:
The detailed explanation for the above-written question is as follows
Question:4(i) Evaluate
Answer:
The detailed explanation for the above-written question is as follows
After rewriting the above equation, we get,
An alternate method,
here you can use first
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
Answer:
We have,
Here a = 5 and n =-3 and m-n = 5
therefore,
By comparing 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
Question: 6(ii) Evaluate
Answer:
The detailed solution for the above-written question is as follows
Question: 7(i) Simplify
Answer:
The detailed solution for the above-written question is as follows
we can write
So, after rewriting the equation,
Question: 7(ii) Simplify.
Answer:
The detailed solution for the above-written question is
we can write 125 =
Now, rewriting the equation, we get
As
NCERT Solutions for Class 8 Maths Chapter 10 Exponents and Powers Exercise 10.2 Page Number: 128 Number of Questions: 4 |
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: 2(i) Express the following numbers in the usual form.
Answer:
This is the usual form.
Question: 2 (ii) Express the following numbers in the usual form.
Answer:
This is the usual form.
Question: 2(iii) Express the following numbers in the usual form.
Answer:
This is the usual form.
Question: 2(iv) Express the following numbers in the usual form.
Answer:
This is the usual form.
Question: 2(v) Express the following numbers in the usual form.
Answer:
This is the usual form.
Question: 2(vi) Express the following numbers in the usual form.
Answer:
17155
Question: 3(i) Express the number appearing in the following statements in standard form.
1 micron is equal to
Answer:
1 micron is equal to
Question: 3(ii) Express the number appearing in the following statements in standard form.
The charge of an electron is 0.000,000,000,000,000,000,16 coulomb.
Answer:
The charge of an electron is 0.000,000,000,000,000,000,16 coulomb.
Question: 3(iii) Express the number appearing in the following statements in standard form.
The size of a bacteria is 0.0000005 m.
Answer:
The size of a bacteria is 0.0000005 m
Question: 3(iv) Express the number appearing in the following statements in standard form.
The size of a plant cell is 0.00001275 m.
Answer:
The size of a plant cell is 0.00001275 m
Question: 3(v) Express the number appearing in the following statements in standard form.
The 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
The topics discussed in the NCERT Solutions for class 8, chapter 10, Exponents and Powers, are:
Here are some important formulas or laws that will help students to solve problems related to Exponents and Powers.
Law of Product:
Law of Quotient:
Law of Zero Exponent:
Law of Negative Exponent:
Law of Power of a Power:
Law of Power of a Product:
Law of Power of a Quotient:
Given below are all the chapter-wise NCERT class 8 maths solutions given in one place for ease of access:
The NCERT solutions for class 8 Maths is one of the essential study materials for students in exam preparation. Check out the Subject-wise NCERT Solutions for Class 8 below.
It is very important to focus on other study resources like NCERT Books and NCERT Syllabus to get an overview of the topics covered in this academic year. Students can use the below links to access the NCERT Syllabus and book PDFs.
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