User Manual
- 2 -
Negative and fractional indices: Learning resource objective
Understand negative and fractional powers
Introduction to negative powers
From p choose Table. Choose SET y and input Start 1, End 4 and Step 1, using l to save your
settings.
x
Y1 2
x
=
Y2 3
x
=
( )
1
2
Y3
x
=
( )
3
2
Y4
x
=
-3
3
2
−
=
3
3
−
=
-2
2
2
−
=
2
3
−
=
-1
1
2
−
=
1
3
−
=
0
0
2
=
0
3 =
1
1
2 =
1
3 =
2
2
2
=
2
3 =
3
3
2
=
3
3 =
4
4
2
=
4
3 =
b.
Expressing the pattern algebraically 𝑎
−𝑛
=
Task
1. Type
Y1 2
x
=
to create a table of values for powers of 2 from 1 to 4.
a. Write the values on the shaded part of the table below.
b. Write down the pattern in the answers as you go up the table (x getting smaller).
c. Use the pattern to predict the values of
2
x
when
0x =
and when x is negative.
d. Change the settings so the table of values shows negative values of x and check your
answers. (Highlight each decimal answer and press
v to show fractional values.)
2. Repeat for the other numbers – is there a similar pattern?
3. How could you express this algebraically?
Follow-up
Write down fractional answers to the following. Choose Run-Matrix mode to check the answers.
a.
4
2
−
=
b.
1
5
−
=
c.
0
2
7
=
d.
2
3
5
−
=
e.
3
1
4
−
=
f.
2
2
7
−
=