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Do NowSimplify each of the exponential expressions
2 33 3 233 323
3 2a a 7b b 23a
4
2
3
3
29
3
2
2
34
8
c
c
53 63 63
5a 8b 6a
23 26 122 23
4 12
1 1
c c
Let’s look at how we can work with expressions such as
124
138
1416
324
238
529
4 16 4 29 25 32
3 34 35 32 24 64
Open the TI-NSPIRE File
• Let’s look at some table values for x1/2. • Look for some special values you might
recognize. What would be another way to express x1/2?
• Look at a graph and click on the line to see what graph has been plotted.
Some things your observed
124 4 2
129 9 3
1216 16 4
1236 36 6
How can you rewrite each of the following with a fractional exponent?
49
121
15
c
1249
12121
1215
12c
Open the TI-NSPIRE File
• Let’s look at some table values for x1/3. • Look for some special values you might
recognize. What would be another way to express x1/3?
• Look at a graph and click on the line to see what graph has been plotted.
Some things your observed
1338 8 2
1331 1 1
How can you rewrite each of the following with a fractional exponent?
13125
13216
13513a
13327 27 3
13364 64 4
3 125
3 216
3 5
3 a
Open the TI-NSPIRE File
• Let’s look at some table values for x1/4. • Look for some special values you might
recognize. What would be another way to express x1/3?
• Look at a graph and click on the line to see what graph has been plotted.
Some things your observed
1441 1 1
14416 16 2
How can you rewrite each of the following with a fractional exponent?
14256
1415
14d
14481 81 3
4 256
4 15
4d
1416 2
Which problems can you rewrite?
124
138
1416
324
238
529
4 16 4 29 25 32
3 34 35 32 24 64
4 2 3 8 2 4 16 2
Now let’s find out how we look at
the others!
Open the TI-NSPIRE File
• Let’s look at some table values for 4x, such as 41, 41.5, 42, 42.5, 43, 43.5, 44, etc.
• Look for some special values you might recognize like 41, 42, 43, 44.
• Look at the value for x = 1.5. Remember this is 41.5. What fractional power could replace 1.5?
1 311.5 2 24 4 4
32 8
324To find a value for we need
to do a little math.
13
24
324
13 24
1264 64 8
13
24or
12
3
4
34
3 324 4
Open the TI-NSPIRE File
• Let’s look at some table values for 16x, such as 161, 161.5, 162, 162.5, 163, 163.5, 164, etc.
• Look for some special values you might recognize. First look at 161, 162, 163
• Look at the value for x = 1.25. What fraction could replace 1.25?
51.25 416 16
14
54
1,048,576
16
5416
15
4
15
4
16
16or
14
15 4
5
16
16
4
5
1,048,576 32
2 32
54
54
16
16
5 5
4416 16
Simplify3
1.5 216 16
13 1322 2
13 32
3
1 3
2
3
2
31
16 16 4096 4096 64
16 4
16
16 16 4
16
6or
3 3216 16
Now can you simplify the rest?
124
138
1416
324
238
529
4 164 29 25 32
3 34 35 32 24 64
4 2 3 8 2 4 16 2
34 8 39 27 23 8 4
1416 2
25
2
32
2 4
24
12
9
9 3
33
1
4
4 4
35
3
32
2 8
122464 64
8
Using the new ideas to solve equations
3 4x
13 4x
3
13
3 4x
1 64
64
x
x
These statements state that the cube root of some number is 4. What operation will undo the cube root?
We’ll cube both sides.
3 64 4 üOur solution checks
Solve this equation3 4 16c
43 16x
3
4 34 343 416 16x
1 32
8
x
x
These statements are the same. How can we undo raising a number to the 4/3 power?
We’ll raise each side to the ¾ power
üOur solution checks 43 348 8 16
Solve this equation4 3x
14 3x
1 3 3 3 3
81
x
x
These statements are the same. How can we undo raising a number to the 4/3 power?
We’ll raise each side to the power of 4
üOur solution checks4 81 3
4
14
4 3x
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