OPERATING WITH INDICES
TASK 1
1
Explore indices using a calculator
Use a calculator to answer these questions.
a
Does 42 + 43 equal 45?
b Does 36 – 34 equal 32?
c
Does 85 + 82 equal 167?
d
Which of these is equal
to 73 × 72?
e Which of these is equal to
f
Does 45 × 46 equal 411?
i
Does 59 ÷ 53 ÷ 52 equal 54?
76
g
2
496
75
495
Does 32 × 53 equal 155?
6
2
10 ÷ 10 ?
14
104
103
13
h Does 22 × 23 × 25 equal 210?
Use your findings above to cross out a word or phrase in each box so that these statements are true.
You may wish to first experiment further using your own calculations with bases and indices.
a
When adding or subtracting numbers with the same base, you can/cannot add or subtract
their powers.
b
When multiplying numbers with the same base, you can/cannot add their powers.
c
When multiplying numbers with different bases, you can/cannot add their powers.
d
When dividing numbers with the same base, you can/cannot subtract their powers.
e
When dividing numbers with different bases, you can/cannot add their powers.
f
When multiplying or dividing numbers with the same base, the base stays the same/changes
in the answer.
TASK 2
Reducing multiplication and division
Use your findings from task 1 to complete these equations.
1
85  8 2  8
4
74  76 
7
411  45  4
10
276  27 2 
TASK 3
2
69  610  6
3
128  12
5
2 4  23  2 6  2
6
34  3  3
8
28  24  2
9
1510 15
11
815  85  83  8
12
379  37  37
10
4
 1214
 153
The power of zero
1
Follow the number patterns to complete the tables below.
2
What do you predict 80 is equal to as a number? ________________________
(Use the power button on your calculator to check by entering 80.)
3
Complete this sentence:
A number raised to the power of zero equals ___________.
4
Now check a special case.
Enter 00 into your calculator. What do you get? ________________________________________
Discuss your findings with the class.