Describe the pattern in the following example. Division Rule - When dividing two powers with the...
-
Upload
valerie-robyn-white -
Category
Documents
-
view
217 -
download
0
Transcript of Describe the pattern in the following example. Division Rule - When dividing two powers with the...
Describe the pattern in the following example.
35
32= =33=3• 3• 3
Division Rule - When dividing two powers with the same base, subtract the exponents
3• 3• 3• 3• 33• 3
67
64=67−4 = 63
a9
a3=a9−3 = a6
x5y7
x2y5= x5
x2⎛
⎝⎜⎞
⎠⎟y7
y5
⎛
⎝⎜⎞
⎠⎟=x5−2y7−5 =x3y2
Describe the pattern in the following example
3
5⎛⎝⎜
⎞⎠⎟
2
=3
5⎛⎝⎜
⎞⎠⎟3
5⎛⎝⎜
⎞⎠⎟
=3• 3
5 • 5=32
52
Power of Quotient Rule - The power of a quotient is equal to the power of the numerator divided by the power of the denominator
42
33⎛
⎝⎜⎞
⎠⎟
3
=42( )
3
33( )3 =
46
39
3p2
4
⎛
⎝⎜⎞
⎠⎟
3
=3p2( )
3
43=33 p6
43
Rule – The power of any non-zero number to the zero power is equal to one!
(Don’t believe me… watch this!!!)
x4
x4=x4−4 =x0
Or….x4
x4=1
Therefore…
1
52=5−2
53
55
5 • 5 • 55 • 5 • 5 • 5 • 5
1
5 2
53−5
5−2
For any non-zero number a and any integer n, a-n is the reciprocal of an.
a−n =1an
x−3 =1
x3
a−3b2c−2
d−3=
1
a3⎛⎝⎜
⎞⎠⎟b2
1
⎛
⎝⎜⎞
⎠⎟1
c2⎛⎝⎜
⎞⎠⎟d 3
1
⎛
⎝⎜⎞
⎠⎟=a−3
1
⎛
⎝⎜⎞
⎠⎟b2
1
⎛
⎝⎜⎞
⎠⎟c−2
1
⎛
⎝⎜⎞
⎠⎟1
d−3⎛⎝⎜
⎞⎠⎟
=b2d 3
a3c2