Download Powerful numbers on the TI

Powerful numbers
Powerful numbers on the TI-15
10 5 is a simple way of writing 10 x 10 x 10 x 10 x 10 = 100 000
To see the powers of 10 use the Op1 action on the calculator:
Set Op1 to be x 10
To do this press keys .
This sets Op1, and the small Op1 icon
on the screen confirms it.
Enter  and the screen shows this.
Repeatedly pressing Op 1 will show all the powers of 10 up to 10 10, and from
there the answer is written only as a power of 10.
[An “overflow error” shows at 1 x 10100.]
Activity: To learn about “Index laws” using the TI-15
When eg 8 is written in the form 2 3, we say 2 to the power 3 , and it is written
in index form.
The 2 is called the BASE of the number and the 3 is called the Power [or
sometimes Index or Exponent].
Copy this table below.
Using your calculator, as necessary, complete the table of powers of 2.
[A simple way to do this is to set Op1 as x2, and record the powers as they
appear on the screen. To set Op1 Press .
Note the first entry is 2^0 and the answer is NOT 0.]
Index form
20
21
22
23
24
Number
Index form
25
26
27
28
29
Number
Index form
2 10
2 11
2 12
2 13
2 15
Number
1
Powerful numbers
Question 1.
Example: Use the calculator to find 2 3 x 2 4
Check if this answer appears in your table.
So 2 3 x 2 4 = 128 = 2 7 from the table.
Copy and complete the table below using this method.
Question
a.
b.
c.
d.
e.
f.
g.
h.
Answer from
calculator
Power form of
answer from
table above
27 x 26
28 x 24
2 0 x 2 11
23 x 24 x 23
28  24
2 12  2 9
28  28
22 + 23
Predict the answer to each of the following and check with you calculator
a. 2 5 x 2 4
b. 2 8 x 2 3
c.
2 11  2 6
Explain what you have noticed
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Question 2.
To calculate (2 5) 2 , care needs to be taken with the use of brackets
Check these calculations:
2^5^2
(2^5)^2
2^(5^2)
Note the very different larger answer in the third form!
2
Powerful numbers
Complete this table using your table of powers of 2.
Question
a
b
c
d
Answer from
calculator
Power
form
(2 4) 3
(2 4) 2
(2 3) 3
(2 3) 4
Predict the answer to each of the following and check with you calculator
a. (2 2 ) 5
b. (2 2 ) 3
c.
(2 3 ) 2
d. 2^3^2
Explain what you have noticed
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Question 3.
In this part the index number can be a fraction.
Calculate 8
1
3
Press keys 
Check 
[Again Brackets are important! ]
Check 
Brackets are not needed if the fraction
part is entered as a fraction.
1
From the table of powers of 2,
1
8 3 = ( 23 ) 3 = 2
Check on your calculator.
3
Powerful numbers
Complete this table using your table of powers of 2.
Question
a
64
b
64
c
Answer from
calculator
Power
form
1
2
1
3
1
42
d
1
(4 2 ) 2
e
1
1024 2
Predict the answer to each of the following and check with your calculator.
a.
16
1
2
b.
1
4 2
(2 )
c.
8
2
3
d.
1 1
2 2
(64 )
Explain what you have noticed
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Question 4.
In this part the index number can be a negative number.
To calculate negative powers of 2, use is made of the  button NOT the .
Check 2 1 
Eg
1
2
To calculate 2 3
Press keys 
Now press  to change the decimal answer to a fraction and simplify if
necessary.
We see 2 3 = 0.125 =
1
1
=
8
23
4
Powerful numbers
Complete this table using your table of powers of 2.
Question
a
2 2
b
c
d
2 5
4 2
16

Answer from
calculator
Power
form
1
2
Predict the answer to each of the following and check with your calculator.
a.
8–2
b.
4–3
c.
16 – 1
d.
3
4 2
Explain what you have noticed
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To summarise the INDEX LAWS
1.
2.
3.
4.
5.
6.
7.
8.
b n is a number written in index form.
 b is the BASE,
 n is the power/index/ exponent.
When multiplying two numbers
 the bases MUST be the same
 the powers are added together
When dividing two numbers
 the bases MUST be the same
 the powers are subtracted
When a number in index form is raised to another power
eg (2 5) 2 the two powers are multiplied ( 210 )
When a power is ZERO, the answer is 1 (Except for 00 which has no
meaning.)
Negatives powers turn the number “upside down”. Ie the reciprocal of
the original number.
Fractional powers generally make the number smaller
eg ½ finds the square root.
These laws do not apply to numbers being added or subtracted.
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