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C. Answer the Following.

1. Using laws of exponents, simplify the following.
5
5
− ( ) ×− ( ) 5 3  −  5 4
0
0
(a) (b) 1 + 2 + 3 0 (c)   (d) (–7) 2 × 7 – 6 – 8
 − ( ) 5 2  4  4 
 
2. Evaluate the following using laws exponential.
3
2
2
3
2
5
2
2
2
5 × 10 × 3 5 7 × 3 × 11 5 3 ( ) ×− ( 2) 2 7 ×( ) 5
(a) (b) (c) (d) 6
6 × 5 7 11 ×× 6 2 × 7
5
73
3
2
53
ab × 2 8 343 32 × 9 2
×
(e) (f)
32
32 × ab 49 2 × 36 2
×
4
p   3 2   9 0  p 3
3. If =   ÷   , find the value of .
2
4
q      
q

n
n
4. If 2 n + 2 – 2 n + 1 + 2 = k × 2 , find the value of k.
5. If 3 1998 – 3 1997 – 3 1996 + 3 1995 = k × 3 1995 , they find value of k.
6. Express the following information in standard form.
(a) In a galaxy there are on an average 100,000,000,000 stars.
(b) The universe is estimated to be about 12,000,000,000 years old.
(c) The distance of the Sun from the centre of the Milky Way Galaxy is estimated to be
300,000,000,000,000,000,000 m.
(d) 60,230,000,000,000,000,000,000 molecules are contained in a drop of water weighing 1.8 gm.
(e) The earth has 1,353,000,000 cubic km of sea water.
(f) The population of India was about 1,210,726,932 in March, 2011.
8
6
7. A baker has 2 cupcakes and 2 doughnuts. How many times more does the baker have cupcakes
than the doughnuts? COMPETENCY BASED QUESTION
6
3
2
8. The number, such as 64 = 8 or 4 or 2 can be written as powers of different bases. Write the number
729 as powers of three different bases.
9. Zoya is a freelancer. She was offered the following payments module to choose form: `(25n – 1) or
n
`(25 – 1) for each n hour she work. Which option she will choose and why?
4 5 1
10. A student said that is the same as . What mistake has the student made? Rectify his mistake
16 5 4
and simplify it correctly.
11. A light year is the distance that light can travel in one year. 1 light year = 9,460,000,000,000 km.
Express one light year distance in scientific notation. The sun is around 28000 light years from the
centre of the Milky Way Galaxy. Convert the distance between the sun and the centre of the galaxy
in km and then express it in scientific notation. COMPETENCY BASED QUESTION
10
12. The average distance between Earth and Jupiter is 5.88 × 10 km. Is the distance between Earth and
the Jupiter greater than or less than or equal to one light year?
13. In our own planet Earth, 361,419,000 square kilometre of area is covered with water and 148,647,000

square kilometre of area is covered by land. Find the difference between area covered with water
to area covered by land by converting these numbers into scientific notation.

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