Transcript Power point exponents

Exponents and nth roots
inverse operations
Exponents and nth roots
What is (y2)(y5)?
It is
(y)(y)
or
(y)(y)(y)(y)(y)(y)(y)
times
(y)(y)(y)(y)(y)
which equals y7
Notice:
(y2)(y5) is y2+5 = y7
When
multiplying,
if the bases
are the
same, add
the
exponents
Exponents and nth roots
What is (y2)3
When the
exponents
It is (y)(y) times (y)(y) times (y)(y) are next to
each other,
Which is (y)(y)(y)(y)(y)(y)
multiply
them
6
Which equals y
Notice that (y2)3 is y(2)(3) = y6
Write this example below slide #2:
2
3
(x y)
=x
=
(2)(3)
6
x
3
y
y
(1)(3)
Exponents and nth roots
What is a5
a2
It is (a)(a)(a)(a)(a)
(a)(a)
Which is (a)(a)(a)
Which equals a3
Notice that a5
a2
is a5-2 = a3
When
dividing, if
the bases
are the
same,
subtract the
exponents
Exponents and nth roots
What is a0
It is equal to 1. This is just a
rule. Any number raised to
the 0 power = 1.
What is
5
 
x xy
6
1
2
x
y7
0
=1
Exponents and nth roots
Write x-m using a positive exponent
This one is easy: make a fraction and put
anything with negative exponents in the
denominator. If nothing is left to put on
the top, write 1 for the numerator.
x-m = 1
xm
Write this example below slide # 5
2
-3
2
(4x y )
=
2
4
-6
4xy
=
4
-6
16x y
=
4
16x
6
y
Exponents and nth roots
Write
1
m
x
using a positive exponent
If the negative exponents are in the denominator, move
them back up to the numerator.
1
m
x
=
x
m
Write this example below slide #7
x2
y -3
2
= x4
y -6
= x4 y 6
Exponents and nth roots
Did you know that
xx
2 1
1
2
Now you do.
Here’s one more:
7
x x
5
5
7
Exponents and nth roots
What is
2
x
2
x
2
2
2
= x x x
1
Exponents and nth roots
Only attempt this one if
you be da bomb (or if
you want to)
Simplify:
Answer:

x


x

1/ 2
3/ 4
1/ 2
3/ 4

y z

5

y z

2
5
Remember
this for
your
homework
Exponents and nth roots
Let’s see what you can do……
4 x2 y
Find the area.
5 x3 y3
A = (L)(W)
Answer: (5)(4) (x)(x)(x)(x)(x) (y)(y)(y)(y)
= 20 x5 y4
Exponents and nth roots
P(t) = P0 ekt is the growth rate formula for populations.
P0 is the number at time 0, t is the time (in years), k is
the growth rate, and P(t) is the population at time t. In
the year 2000, the population of the world was
approximately 6 billion. If the population growth rate
of the world is approximately 1.3%, what will the
population be in the year 2015?
Exponents and nth roots
Step 1. Write down what each letter stands for
P(t) is the population after t years (what we are
looking for)
k is the growth rate: (1.3% = 1.3/100 = .013)
t is the time in years: (2000 2015 is 15 years)
e is a button on your calculator (ex)
P0 is the number at time 0 (population in year
2000 which is 6,000,000,000 = 6 x 109)
Exponents and nth roots
Now plug in the numbers into the equation:
P(t) = (6,000,000,000)(e(.013)(15))
= 7291865918.94 (in standard mode)
= 7.3 x 109 (in scientific mode)