Download Simplify: 2(2√4)-2

September 10, 2015
Essential Question:
1. How do you use zero and negative
exponents?
2. How do you find cube roots?
Videos:
What do you do with a negative exponent?
What do you do with a zero exponent?
How will you see this on the Keystone Exam?
Simplify: 2(2√4)-2
a. 1/8
How do you simplify an expression with
negative exponents?
b. 1/4
c. 16
d. 32
New Rules....
New Stuff.....Definition of Zero Exponent
Any negative number raised to an even power will be _____
Ex.
(-2)
(-3)
2
(-1)
4
(-4)
6
(-2)
2
6
Any negative number raised to an odd power will be ______
In words:
a to the zero power is 1 (when a ≠ 0)
Algebra:
a0 = 1
Examples:
50 = 1
Be Careful:
00 = undefined
3
(-3)
5
(-1)
9
(-4)
3
(-2)
3
x0 = 1
(4x4y18)0 = 1
More Examples:
4x5y12z130
Ex.
(-2)
How do you evaluate negative exponents?
0
vs.
4x5y0z130
2
September 10, 2015
New Stuff.....Definition of Negative Exponents
In words: a-n is the reciprocal of an when a ≠ 0
1
Backwards: 1-n = an
Algebra: a-n = an
a
Example: 2-1 =
1
21
Example:
Examples.....
Problem
Write answer using only positive exponents. Always simplify.
x4y-2
1
= 31
3-1
(x2y-1)-1
How does this work with variables?
Answer: Just take the variable to the opposite "level" and make exponent
positive.
3 10 -9
-3
-5
x
y7
x
y-7
xy z
a-2v-5w10
Simplify...write your answers using only positive exponents.
(2x)-3y5
x5y-2
Examples with numbers....
Problem
(x-4y3)-5
23
x3y-2z0
x-4y8
(3x-2y5)-2
2-3
(-4)-2
Rewrite with positive exponents..........then evaluate
September 10, 2015
Examples.....
Problem
Evaluate....(ie. write the answer w/o exponents)
Write with positive exponents..................Then evaluate
2 -1
5
( (
5-2
((
4-1
43
1
3-2
3-2
3-5
8
9
-2
Be Careful.....what does your negative exponent "touch" ?
Back to zeros.....Examples.....
Problem
(3x )
5 -4
3(x5)-4
3x-5
Evaluate
Think.....
04
Think.....
40
Think.....
0-3
September 10, 2015
Video:
Simplifying a cube root
Cube root of a non-perfect cube.
Practice: Cube roots