bell work8/25/14 evaluate the expression. powers and exponents tswbat: evaluate an expression that...
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Bell Work 8/25/14Evaluate the expression.
1. 5 4 2. 7 3 3. 4 6 2
304.
6
455.
596
6.4
Powers and Exponents
TSWBAT: evaluate an expression that has an exponent.
04/20/23
Students understand and use such operations as taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power. They understand and use the rules of exponents.
1.41.5 Roots & Irrational
Numbers
TSWBAT: find the root of a number.
Warm-UpSimplify the expression.
31. 5
125
5 5 5 4
2. 2
16
2 2 2 2 3
3. 3
27
3 3 3 25 5 4 4 9 3
24. 9
81 9 9
25. 9
81
9 9
27
6.3
49
9
7 7
3 3 81
Notes• Definitions
- Power= an expression written with a base and an exponent.
Ex.
25- Base
= the number that is used as a factor.
base
- Exponent= tells how many times the base is going to be a factor.
exponent
25
25
Ex.
5 5
Notes
Now you try.
34
64
Ex.
4 4 4
Simplify each expression.
42
16
Ex.
2 2 2 2 3
2
8
Ex.
2 2 2 16 4 4 4 4 2
35
125
Ex.
5 5 5 3
3
27
Ex.
3 3 3 4
3
81
Ex.
3 3 3 3 25 5 9 3 9 9
Notes
Now you try.
27
49
Ex.
7 7
Simplify each expression.
27
49
Ex.
7 7
23
4
9
16
Ex.
3 3
4 4
49
26
36
Ex.
6 6
26
36
Ex.
6 6
25
8
25
64
Ex.
5 5
8 8
36
Notes
Now you try.
3 22 ____ 3Ex.
2 2 2
Compare with <, >, or =.
4 28
3 3
9
2 45 ____ 2 Ex.
5 5 25
2 2 2 2
4 416
3 23 ____ 4Ex.
3 3 3
9 327
4 4
16
223 ____ 3Ex.
3 3
9
3 3 9
Notes• Definitions
- Square Root= What number times itself equals the radicand.
Ex.
9 3- Perfect Square
= a number whose square root is a whole number.
Ex.0, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100
- Radicand= The number inside of the square root symbol.
Ex.9 = The radicand is 9.
Notes
Ex.36 6 Positive Root
Ex.36 6
Ex.36 6
Negative Root
Positive & Negative Root
Ex.36 No Solution No real number times ITSELF
is negative.
1 1
4 2
9 3
16 4
25 5
36 6
49 7
64 8
81 9
100 10
121 11
144 12
Make a table. Find the square root.
Notes
Ex.
49
Find each root.
7
Ex.
255
Ex.
81No Solution
Ex.
366
Ex.
10010
Ex.
9
Now you try.
No Solution
Notes
Ex.9
25
Find each root.
3
5
Now you try.
9
25
Ex.49
36
7
649
36
Ex.16
81
4
9
16
81
Ex.1
16
1
41
16
Notes• Cube Root
= What number times itself 3 times equals the radicand.
3 1 1 3 8 2 3 27 3 3 64 4 3 125 5Make a table. Find the cube root.
Ex.3 27
3
Ex.3 64
4
Ex.3 125
5
Ex.3 8
2
Ex.3 1
1
Ex.3 216
Now you try.
6
3
Notes
Ex.
38
27
Find each root.
2
3
Now you try.
3
3
8
27
Ex.
3125
64
5
4
3
3
125
64
Ex.
31
64
1
4
3
3
1
64
Ex.
327
125
3
5
3
3
27
125
Summary
To find the square root of a number just figure out which number times _____ equals the radicand. If it is a fraction, just find the square root of the top and _______ separately. If it is a _____ root do the same thing except find the number that times itself three times equals the _________.
itself
bottom cube
radicand
A power is an expression that has an _________. The base is the factor, and the exponent tells you how many _______there are. To solve a power, just write down the base as many times as the exponent says, then ________.
exponentfactors
multiply
HomeworkSimplify.
1. 16 2. 81 3. 100
4. 36 5. 49 6. 25
817.
25
18.
25
1009.
49
310. 27 311. 125 312. 125
38
13.27
31
14.64
327
15.125
Today’s Homework
1. Pencil ONLY.2. Must show all of your work.
• NO WORK = NO CREDIT3. Must attempt EVERY problem.4. Always check your answers.
Rules for Homework
Today’s Homework
1. Pencil ONLY.2. Must show all of your work.
• NO WORK = NO CREDIT3. Must attempt EVERY problem.4. Always check your answers.
Rules for Homework
Complete the Ticket Out the Door without talking!!!!!
Talking = time after the bell!
Ticket Out the Door
Put your NAME on the paper.
When finished, turn your paper face DOWN.
Evaluate the expression.
24
Find the root.
36
Class WorkEvaluate the expression.
31. 2 8 22. 3 9 23. 7 49
34. 5 125 45. 3 81 56. 2 32
27. 3 9 3
8. 3 27 49. 3 81
210. 8 64 511. 3 243 312. 4 64
25
13.3
25
9
24
14.3
16
9
24
15.3
16
9
2 316. 6 ____ 3Compare with <, >, or =.
2 517. 2 ____ 1 2 318. 8 ____ 4