Transcript Power point exponents
Exponents and nth roots
inverse operations
Exponents and nth roots
What is (y 2 )(y 5 )?
It is (y)(y) times (y)(y)(y)(y)(y) or (y)(y)(y)(y)(y)(y)(y) which equals y 7
When multiplying, if the bases are the same, add the exponents
Notice: (y 2 )(y 5 ) is y 2+5 = y 7
Exponents and nth roots
What is (y 2 ) 3 It is (y)(y) times (y)(y) times (y)(y) Which is (y)(y)(y)(y)(y)(y)
When the exponents are next to each other, multiply them
Which equals y 6 Notice that (y 2 ) 3 is y (2)(3) = y 6
Write this example below slide #2:
(x 2 y) 3 = x (2)(3) y (1)(3) = x 6 y 3
Exponents and nth roots
What is a 5 a 2 It is (a)(a)(a)(a)(a) (a)(a) Which is (a)(a)(a) Which equals a 3 Notice that a 5 a 2 is a 5-2 = a 3
When dividing, if the bases are the same, subtract the exponents
Exponents and nth roots
What is a 0
It is equal to 1. This is just a rule. Any number raised to the 0 power = 1.
What is
5
x
2 1
y
7 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 x m
Write this example below slide # 5
(4x
2
y
-3
)
2
= 4
2
x
4
y
-6
= 16x
4
y
-6
= 16x
4
y
6
Exponents and nth roots
1
x
If the negative exponents are in the denominator, move them back up to the numerator.
1
x
m
=
x m
Write this example below slide #7
x
2
y
-3 2
= x y
4 -6
= x
4
y
6
Exponents and nth roots
Did you know that
2
x
1
x
2 1
Now you do.
Here’s one more:
7
x
5
x
7 5
Exponents and nth roots
What is
2
x
2
x
2 =
x
2 2
x
1
x
Exponents and nth roots
Only attempt this one if you be da bomb (or if you want to) Simplify:
1/ 2
x
3/ 4 5
y z
2
Remember this for your homework
Answer: 1/ 2
x
3/ 4 5
y z
Exponents and nth roots
Let’s see what you can do…… Find the area.
5 x 3 y 3 4 x 2 y A = (L)(W) Answer: = 20 x 5 (5)(4) y 4 (x)(x)(x)(x)(x) (y)(y)(y)(y)
Exponents and nth roots
P(t) = P 0
P 0
e kt is the growth rate formula for populations. 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 ( e x ) P 0 is the number at time 0 (population in year 2000 which is 6,000,000,000 = 6 x 10 9 )
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 10 9 (in scientific mode)