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Published on: 03/10/2019
Exponents and Powers
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Take MCQ Mathematics Test
1.
Expand the following numbers: 300.05
2.
Expand the following numbers: 207.52
3.
By What number \((\frac{-1}{2})^{-3}\) be divided, so that the quotient may be \((\frac{4}{5})^{-2}\)?
4.
Find the value of (5-1-2-1)-1 - (2-1-5-1)
5.
If \(\frac{p}{q}=(\frac{3}{7})^{-3}\times (\frac{21}{12})^{-3}\) then find \((\frac{p}{q})^{-1}\).
6.
While studying her family's history. Shikha discovers records of ancestors 12 generations back. She wonders how many ancestors she has had in the past 12 generations. She starts to make a diagram to help her figure this out. The diagram soon becomes very complex.
(a) Make a table showing the number of ancestors in each of the 12 generations.
(b) Write an equation for the number of ancestors in a given generation n.
7.
Find the value of x-3 , if x = (100)1- 4 + (100)0.
8.
Investigating Solar System The table shows the average distance from each planet in our solar system to the Sun.
| Planet | Distance from Sun (km) | Distance from Sun in (km) Standard Notation |
| Earth | 149600000 | |
| Jupiter | 778300000 | |
| Mars | 227900000 | |
| Mercury | 57900000 | |
| Neptune | 4497000000 | |
| Pluto | 5900000000 | |
| Saturn | 1427000000 | |
| Uranus | 2870000000 | |
| Venus | 108200000 |
(a) Write the distance from each planet to the Sun in standard notation.
(b) Arrange the planets from closest to the Sun to farthest from the Sun.
9.
The distance between the Earth and a star is 7.83 x 105 km. Convert it into usual form.
10.
Express the product of 1.3x104 and 3.4x10-2 in the standard form.
1.
\(3\times 10^{2}+5\times 10^{-2}\)
2.
\(2\times 10^{2}+7\times 10^{0}+5\times 10^{-1}+2\times 10^{-2}\)
3.
\(-\frac{128}{25}\)
4.
\(-\frac{109}{30}\)
5.
\(\frac{27}{64}\)
6.
(a) Generation table (according to the diagram) showing the number of ancestors are given below:
| Generation | Ancestor |
|---|---|
| 1 | 2 |
| 2 | 22 |
| 3 | 23 |
| 4 | 24 |
| 5 | 25 |
| 6 | 26 |
| 7 | 27 |
| 8 | 28 |
| 9 | 29 |
| 10 | 210 |
| 11 | 211 |
| 12 | 212 |
(b) Equation for the number of ancestors in generation n is 2n [according to the part (a)].
7.
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, \(x^{-3}=\frac{1}{(100)^{-3}}\times \frac{1}{(100)^{-3}}\times \frac{1}{(100)^{-3}}\)
⇒ \(x^{-3}=\frac{1}{(100)^{-(3+3+3)}}\)
⇒ \(x^{3}=\frac{1}{(100)^{-9}} \Rightarrow x^{-3}=(100)^{9}\)
8.
(a) Earth ➝ 1.496 x 108 km
Jupiter ➝ 7.783 x 108 km
Mars ➝ 2.279 x 108 km
Mercury ➝ 5.79 x 107 km
Neptune ➝ 4.497 x 109 km
Pluto ➝ 5.9 x 109 km
Saturn ➝ 1.427 x 109 km
Uranus ➝ 2.87 x 109 km
Venus ➝ 1.082 x 108 km
(b) On arranging the planets from closest to the Sun to farthest from the Sun, we get following order
Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto.
9.
783000
10.
4.42 X102
8th Standard CBSE Syllabus & Materials
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CBSE 8th Standard CBSE Subjects
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