What to do:

1 Use the graphing package to draw the graphs of y=8x and x=^23 on the same

set of axes.

Find the value of 8

(^23)
by locating the intersection of the two graphs.
2 Use the rule (am)n to simplify
¡
82
¢^13
and
³
8
13 ́^2
.
3 Copy and complete: i
¡
82
¢^13
=^3
p
82 =:::::: ii
³
8
(^13)
́ 2

¡p 3
8
¢ 2
=::::::
4 Use 3 to write a
mn
in two different forms.
You should have discovered that a
mn
= n
p
am or
¡pn
a
¢m
.
In practice we seldom use these laws, but they do help to give meaning to rational exponents.
Example 2 Self Tutor
Simplify: a 27
(^43)
b 16 ¡
(^34)
a 27
(^43)
=(3^3 )
(^43)
=3^4
=81
b 16 ¡
(^34)
=(2^4 )¡
(^34)
=2¡^3

1

23

=^18

EXERCISE 28A

1 Evaluate without using a calculator:

a 4

(^12)
b 4
¡^12
c 16
(^12)
d 16
¡^12
e 25
(^12)
f 25
¡^12
g 8
(^13)
h 8
¡^13
i 64
(^13)
j 64
¡^13
k 32
(^15)
l 32
¡^15
m 125
(^13)
n (¡125)
(^13)
o (¡1)
(^12)
p (¡1)
(^13)
2 Write the following in index form:
a
p
10 b p^110 c^3
p
15 d

1

p (^315)
e^4
p
19 f

1

p 419 g

p (^513) h 1
p (^513)
3 Use your calculator to evaluate, correct to 3 significant figures where necessary:
a^3
p
64 b^4
p
81 c^5
p
1024 d^3
p
200
e^4
p
400 f^5
p
1000 g^7
p
128 h^3
p
10 : 83
4 Without using a calculator, find the value of the following:
a 8
(^43)
b 8 ¡
(^23)
c 4
(^32)
d 4 ¡
(^32)
e 27
(^23)
f 27 ¡
(^23)
g 32
(^25)
h 32 ¡
(^35)
i 64
(^56)
j 125 ¡
(^23)
k 81
(^34)
l 81 ¡
(^34)
GRAPHING
PACKAGE
Exponential functions and equations (Chapter 28) 567
IGCSE01
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Y:\HAESE\IGCSE01\IG01_28\567IGCSE01_28.CDR Monday, 27 October 2008 2:43:36 PM PETER