8th Standard CBSE Syllabus & Materials
8th Standard CBSE
CBSE 8th Social Science Theme D - Factors of Production - New Model Questions Papers Study Material - QB365 Set A
NEW8th Standard CBSE
CBSE 8th Social Science Theme C - Universal Franchise and India's Electoral System - New Model Questions Papers Study Material - QB365 Set A
NEW8th Standard CBSE
CBSE 8th Social Science Theme B - The Rise of the Marathas - New Model Questions Papers Study Material - QB365 Set A
NEW8th Standard CBSE
CBSE 8th Social Science Theme B - Reshaping India's Political Map - New Model Questions Papers Study Material - QB365 Set A
NEW8th Standard CBSE
CBSE 8th Social Science Theme A - Natural Resources and Their Use - New Model Questions Papers Study Material - QB365 Set A
NEW8th Standard CBSE
CBSE 8th Science Keeping Time with Skies - New Model Questions Papers Study Material - QB365 Set A
Published on: 26/11/2019
Exponents and Powers
Download CBSE Class 8th Standard CBSE Mathematics question papers, sample papers, important questions, and previous year solved papers in PDF format. Get free study materials, NCERT solutions, and exam preparation resources for Class 8th Standard CBSE Mathematics
Questions + Answers key
Take MCQ Mathematics Test
1.
Express the following numbers in usual form: 7.54 \(\times\) 10-4
2.
Write each of the following in standard form: 0.00001278
3.
Find the value of m for which \(5^{m}\div 5^{-3}=5^{5}\)
4.
Simplify and write in exponential form.
\(3^{2}\times 3^{-5}\times 3^{6}\)
5.
Find the multiplicative inverse of the following:
10-100
6.
Express 2.0001 \(\times\) 109 in usual form.
7.
Simplify: \({ \left[ { \left( \frac { -4 }{ 5 } \right) }^{ -2 } \right] }^{ 2 }\)
8.
Compare the size of a red blood cell which is 0.000007 m to that of a plant cell which is 0.0000129 m.
9.
Express \(\frac{1.5\times 10^{6}}{2.5\times 10^{4}}\) In the standard form.
10.
Find the standard form of the number 0.0005+0.0085.
11.
Find the value of x, if 2x÷ 23 = 2-1
12.
Express the following numbers in standard form 5463
13.
Consider a quantity of a radioactive substance. The fraction of this quantity that remains after t half-lives can be found by using the expression 3-t.
(a) What fraction of substance remains after 7 half-lives?
(b) After how many half-lives, will the fraction be \(\frac{1}{243}\) of the original?
14.
Express the product of 1.3x104 and 3.4x10-2 in the standard form.
15.
Which of the following is equal to [100 - 99\(°\)] \(\times\) 100?
10000
100
9900
99000
16.
Which of the following is the standard form of 0.00001275?
1.275 \(\times\) 10-5
1.275 \(\times\) 10-5
127.5 \(\times\) 10-7
127.5\(\times\) 107
17.
The usual form of 2.08 x 10-5 is
0.0000208
0.000028
0.000208
0.0002080
18.
The value of 35÷ 3-8 is
313
3-13
3-3
33
19.
5-2 can be written as
\(\frac{1}{5}\)
\(\frac{1}{5^{2}}\)
52
-\(\frac{2}{5}\)
1.
\(7.54 \times 10^{-4}=\frac{7.54}{10^{4}}=\frac{7.54}{10000}=0.000754\)
2.
1.278 \(\times\)10-5
3.
Given, \(5^{m}\div 5^{-3}=5^{5}\) ⇒ \(\frac{5^{m}}{5^{-3}}=5^{5}\)
⇒ 5m-(-3) = 55 \([\because \frac{a^{m}}{a^{n}}=a^{m-n}]\)
⇒ 5m+3 = 55
On comparing the powers of 5 of both sides, we get
m + 3 = 5 ⇒ m = 5 - 3 ⇒ m = 2
Hence, the value of m is 2.
4.
32 \(\times\) 3-5 \(\times\) 36 = 32+(-5)+6 = 38-5 = 33
5.
Multiplicative inverse of 10-100 is 10100.
6.
We have
\(2.0001\times { 10 }^{ 9 }=\frac { 20001 }{ 10000 } \times 1000000000\)
= 20001 \(\times\) 100000
= 2000100000
Thus, 2.0001 \(\times\) 109 = 2000100000
7.
Since, \({ \left( \frac { a }{ b } \right) }^{ m }=\frac { { a }^{ m } }{ { b }^{ m } } \quad and\quad { (a }^{ m })^{ n }={ a }^{ mn }\)
\(\therefore \quad { \left[ { \left( \frac { -4 }{ 5 } \right) }^{ -2 } \right] }^{ 2 }={ \left( \frac { -4 }{ 5 } \right) }^{ -2\times 2 }={ \left( \frac { -4 }{ 5 } \right) }^{ -4 }={ \left( \frac { 5 }{ -4 } \right) }^{ 4 }\)
\(=\frac { 5\times 5\times 5\times 5 }{ (-4)\times (-4)\times (-4)\times (-4) } =\frac { 625 }{ 256 } \)
Thuss, \({ \left[ { \left( \frac { -4 }{ 5 } \right) }^{ -2 } \right] }^{ 2 }=\frac { 625 }{ 256 } \)
8.
Size of red blood cell = 0.000007 m
\(=\frac { 7 }{ 1000000 } =7\times { 10 }^{ -6 }m\)
Size of the plant cell = 0.0000129 m
\(=\frac { 129 }{ 10000000 } m=\frac { 1.29\times { 10 }^{ 2 } }{ 10000000 } m=1.29\times { 10 }^{ -5 }m\)
Now \(\frac { 7\times { 10 }^{ -6 } }{ 1.29\times { 10 }^{ -5 } } =\frac { 7\times { 10 }^{ -1 } }{ 1.29 } \)
\(=\frac { 7\times { 10 }^{ -1 } }{ 1.3 } =\frac { 0.7 }{ 1.3 } =\frac { 1 }{ 2 } \) (approx.)
Thus, the size of a red blood cell is half of the plant cell size.
9.
We have, \(\frac{1.5\times 10^{6}}{2.5\times 10^{4}}\)=\(\frac{1.5\times 10^{2}\times10^{4}}{2.5\times 10^{4}}\)
=\(\frac{150}{2.5}\times10^{4-4}=\frac{150}{2.5}\times 10^{0}\)
= 60 x 1 = 60 = 6.0 x 101 = 6.0 x 10
10.
9x 10-3
11.
2
12.
5.463x103
13.
The fraction of substance remains after 7 half- lives =3-7=\(\frac{1}{3^{7}}\)
ஃ \(3^{-x}=\frac{1}{243}=\frac{1}{3\times3\times3\times3\times3}=\frac{1}{3^{5}}\)
⇒ \(3^{-x}=3^{-5}\)
⇒ \((3)^{-x}=(3)^{-5}\)
⇒ -x=-5 [∵ bases are same]]
Hence, after 5 half-lives, the fraction will be \(\frac{1}{243}\) of the original.
14.
4.42 X102
15.
(c)
9900
16.
(a)
1.275 \(\times\) 10-5
17.
(a)
0.0000208
18.
(a)
313
19.
(b)
\(\frac{1}{5^{2}}\)
8th Standard CBSE Syllabus & Materials
8th Standard CBSE
CBSE 8th Science Particulate Nature of Matter - New Model Questions Papers Study Material - QB365 Set A
NEW8th Standard CBSE
CBSE 8th Science Pressure, Winds, Stroms and Cyclones - New Model Questions Papers Study Material - QB365 Set A
NEW8th Standard CBSE
CBSE 8th Mathematics Quadrilaterals - New Model Questions Papers Study Material - QB365 Set A
NEW8th Standard CBSE
CBSE 8th Mathematics A story of Numbers - New Model Questions Papers Study Material - QB365 Set A
CBSE 8th Standard CBSE Subjects
CBSE Standards
