Download Exponents and Powers

Exponents and Powers
Main Concepts and Results:
Exercise
1) Find the multiplicative inverse of the following.
2) Expand the following numbers using exponents.
(i)
1025.63
(ii)
1256.249
3) Write down the laws of exponents.
4) Find the value of
(i)
2
(ii) 1/3
5) Simplify
6) Express 4 as a power with the base 2.
7) Simplify and write the answer in the exponential form.
8) Find m so that
9) Find the value of (2/3
10) Simplify
.
11) Evaluate.
12) Simplify and express the result in power notation with positive exponent.
13) Find the value of.
14) Evaluate
15) Find the value of m for which 5
16) Evaluate
÷5
= 5 .
17) Simplify.
18) Write the following numbers in standard form.
(i)
0.000000564
(ii) 0.0000021
19) Write all the facts given in the standard form.
(iii) 21600000
(iv) 15240000
20) Express the following numbers in standard form.
(i)
0.000035
(ii) 4050000
21) Express the following numbers in usual form.
22) Express the following numbers in standard form.
23) Express the following numbers in usual form.
24) Express the number appearing in the following statements in standard form.
25) In a stack there are 5 books each of thickness 20mm and 5 paper sheets each of thickness
0.016 mm. What is the total thickness of the stack?
26) Some migratory birds travel as much as 15,000 km to escape the extreme climatic conditions
at home. Write the distance in metres using scientific notation.
27) Pluto is 59,1,30,00, 000 m from the sun. Express this in the standard form.
28) Special balances can weigh something as 0.00000001 gram. Express this number in the
standard form
29) A sugar factory has annual sales of 3 billion 720 million kilograms of sugar. Express this
number in the standard form.
30) The number of red blood cells per cubic millimetre of blood is approximately 5.5 million. If
the average body contains 5 litres of blood, what is the total number of red cells in the
body? Write the standard form. (1 litre = 1,00,000 mm3)
31) Express each of the following in standard form:
32) Find x so that
33) By what number should
34) Find the value of n.
be divided so that the quotient may be
?
(i)
(ii)
35) A new born bear weighs 4 kg. How many kilograms might a five year old bear weigh if its
weight increases by the power of 2 in 5 years?
36) If
37) The cells of a bacteria double in every 30 minutes. A scientist begins with a single cell. How
many cells will be there after
(a) 12 hours
(b) 24 hours
38) The cells of a bacterium double itself every hour. How many cells will there be after 8 hours,
if initially we start with 1 cell. Express the answer in powers.
39) A half-life is the amount of time that it takes for a radioactive substance to decay to one half
of its original quantity.
40) One Fermi is equal to 10–15 metre. The radius of a proton is 1.3 Fermis. Write the radius of a
proton in metres in standard form.
41) Find x.
42) If a = – 1, b = 2, then find the value of the following:
43) Express each of the following in exponential form:
44) A particular star is at a distance of about 8.1 × 1013 km from the Earth. Assuring that light
travels at 3 × 108 m per second, find how long does light takes from that star to reach the
Earth.
45) Use the properties of exponents to verify that each statement is true.
46) There are 86,400 seconds in a day. How many days long is a second? Express your answer in
scientific notation.
47) About 230 billion litres of water flows through a river each day. How many litres of water
flows through that river in a week? How many litres of water flows through the river in an
year? Write your answer in standard notation
48) Simplify:
49) Fill in the blanks to make the statements true.
(I)
(II)
50) Very small numbers can be expressed in standard form using positive exponents.True or
false?
51) Simplify
52) Find x so that
53) The value of
(a) 2
(b) 10/3
(c) 2
+1
(d) 10
54) The solution of 3
= 1/9
(a) 5/2
(b) 5
(c) 1
Multiple Choice Questions:
(d) 7/3