Page 80 - ICSE Math 7

4. Express each of the following using only positive exponents.
a –2 c 3
–3
–1
–2
–1
(a) x + x = 1 (b) l + m = n –1 (c) + = 0
b –3 d –4
–1 2
–4
4
3
5. Show that: 3 × x × (9 ) × x × x = 1
5
1
6 ab c × ( a bc ) 12 1
4 2
3 −
4
2 −
2 −
−
6. Show that: =
a () 1 12 b () − 2 3 c 1 2
7. Simplify.
    –2   –6  –1 2 3 2 3
3

7 2
9
3

(a) - 3 ÷ - 3 × - 3 (b)      (c) 25  x  ( xy z ) ÷ 5x 2  xy 
2 22
3
2 
5 5 5     7      y   z 2 





8. Determine the value of x in  2  3 ×  2  − 6 =  2  2 −x 1 .
 
 
 
 3   3   3 
9. If x = –2 and y = 2, find the value of the following. –3
2
2 –2
3 2
–3
2 2
(a) (x ) + (y ) (b) (x ) + xy + 2x (c) 6x + 4y 3 (d) 36 x
–4
20 y
10. Simplify the following.
  3  3  9  − 2    − 2  2  8    x  r  x  p  x  q
p
r
q
(a)    ×    ÷    ÷   (b)  q  ×  r  ×  p 


   5   25      9   27   x   x   x 
 3  − 2  9  3  1  − 2 (6ab c ) (4abc )
2
33 72
25 63
(c)  1  ×   ×   (d)
67 52
 5 −   10   10  (12ab c )
THINK SMART
12
1. An adult person has roughly 24 × 10 red blood cells. The average diameter of each of these
–9
cells is 8 × 10 km. If these cells are placed end to end, how long would the line be?
4
2. A star in the Milky Way galaxy is 7 × 10 light years away from the earth and a light year is
12
approximately 5.8 × 10 miles. Find out in scientific form the distance of the star from the earth
in miles.
3. Heavier elements like iron have greater density (in grams per cubic centimetre) than lighter
elements such as nitrogen. The densities of some of the elements are given in the following table.
Can you arrange them in descending order (from heaviest to lightest)?
Element Density
Oxygen 1.429 × 10 –3
Hydrogen 8.388 × 10 –5
Helium 1.764 × 10 –4
Nitrogen 1.2506 × 10 –3
Copper 8.96
Chlorine 2.95 × 10 –3
66