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Exponents and nth rootsinverse operations
Exponents and nth roots
What is (y2)(y5)?
It is (y)(y) times (y)(y)(y)(y)(y)
or (y)(y)(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
What is (y2)3
It is (y)(y) times (y)(y) times (y)(y)
Which is (y)(y)(y)(y)(y)(y)
Which equals y6
Notice that (y2)3 is y(2)(3) = y6
Exponents and nth roots
When the exponents are next to each other, multiply them
Write this example below slide #2:
(x2y)3 = x (2)(3) y (1)(3)
= x6 y3
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 is a5-2 = a3
a2
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 1
265
7
xx xy
y
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
(4x2y-3)2 = 42x4y-6
= 16x4y-6
= 16x4
y6
Exponents and nth roots
Write using a positive exponent
If the negative exponents are in the denominator, move them back up to the numerator.
1mx
1mx
=mx
Write this example below slide #7
x2
y -3
2
= x4
y -6
= x4 y 6
Exponents and nth roots
Did you know that
Now you do.
Here’s one more:
1
2x x
57 5 7x x
2 1
Exponents and nth roots
What is 2x
2x =2
12x x x 2
Only attempt this one if you be da bomb (or if you want to)
Simplify: 1/ 2
53/ 4x y z
2
Answer:
1/ 253/ 4x y z
Exponents and nth roots
Remember this for your homework
Let’s see what you can do……
Find the area.
Exponents and nth roots
4 x2 y
5 x3 y3
Answer: (5)(4) (x)(x)(x)(x)(x) (y)(y)(y)(y) = 20 x5 y4
A = (L)(W)
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)
Exponents and nth roots
