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Published on: 23/09/2019
Exponents and Powers
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Questions + Answers key
Take MCQ Mathematics Test
1.
Find the value of x, if 2x÷ 23 = 2-1
2.
Write each of the following numbers in usual form.
3.517x106
3.
Express the following numbers in standard form 70000
4.
If 32x-1÷ 9 = 27, find the value of x.
5.
By What number \((\frac{-1}{2})^{-3}\) be divided, so that the quotient may be \((\frac{4}{5})^{-2}\)?
6.
Find the multiplicative increase of X2, if \((\frac{2}{5})^{-3}\times (\frac{2}{5})^{5}=(\frac{2}{5})^{x}\)
7.
If a = - 1and b = 2, then find the value of the following:
(i) ab + ba
(ii) ab - ba
(iii) ab x ba
(iv) ab ÷ ba
8.
Find the value of x-3 , if x = (100)1- 4 + (100)0.
9.
Fill in the blanks.
10.
Express the product of 1.3x104 and 3.4x10-2 in the standard form.
1.
2
2.
3517000
3.
7x104
4.
3
5.
\(-\frac{128}{25}\)
6.
\(\frac{1}{4}\)
7.
(i) We have, ab + ba = (-1)2 + (2)-1= 1+\(\frac{1}{2}\)
=\(\frac{2+1}{2}=\frac{3}{2}\)
(ii) We have, ab - ba=(-1)2-(2)-1 [∵ an=\(\frac{1}{a^{n}}\)]
=1-\(\frac{1}{2}\)=\(\frac{2-1}{2}=\frac{1}{2}\)
(iii) We have,ab x ba=(-1)2x(2)-1=1x\(\frac{1}{2}\)=\(\frac{1}{2}\) [∵ an=\(\frac{1}{a^{n}}\)]
(iv) We have, ab ÷ ba=(-1)÷(2)-1=\((-1)^{2}\times \frac{1}{(2)^{-1}}\)
=1x2=2 [∵ \(\frac{1}{a^{-n}}\)=an]
8.
Given, x =(100)1- 4 + (100)0
x=(100)-3 ÷ 1 [∵ (a)0=1]
⇒ x=(100)-3\(\times \frac{1}{1}\)
⇒ x=\(\frac{1}{(100)^{3}}\times \frac{1}{1} \quad [\because a^{-m}=\frac{1}{a^{m}}]\)
⇒ x=\(\frac{1}{(100)^{3}}\)
Now, \(x^{-3}=\frac{1}{(100)^{-3}}\times \frac{1}{(100)^{-3}}\times \frac{1}{(100)^{-3}}\)
⇒ \(x^{-3}=\frac{1}{(100)^{-(3+3+3)}}\)
⇒ \(x^{3}=\frac{1}{(100)^{-9}} \Rightarrow x^{-3}=(100)^{9}\)
9.
We have, 144 x 2-3 = \(\frac{144}{2^{3}}=\frac{12\times 12}{2\times2\times 2 }=18\)
Now, 18X12-1=\(\frac{18}{12}=\frac{3}{2}\)
Again, \(\frac{3}{2}\times 3^{-2}=\frac{3}{2}\times \frac{1}{3^{2}}=\frac{1}{6}\)
So,
10.
4.42 X102
8th Standard CBSE Syllabus & Materials
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CBSE 8th Standard CBSE Subjects
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