exponents and nth roots inverse operations. exponents and nth roots what is (y 2 )(y 5 )? it is...
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![Page 1: 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)](https://reader033.vdocuments.us/reader033/viewer/2022061506/56649ee55503460f94bf41ae/html5/thumbnails/1.jpg)
Exponents and nth rootsinverse operations
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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
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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
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Write this example below slide #2:
(x2y)3 = x (2)(3) y (1)(3)
= x6 y3
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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
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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
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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
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Write this example below slide # 5
(4x2y-3)2 = 42x4y-6
= 16x4y-6
= 16x4
y6
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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
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Write this example below slide #7
x2
y -3
2
= x4
y -6
= x4 y 6
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Exponents and nth roots
Did you know that
Now you do.
Here’s one more:
1
2x x
57 5 7x x
2 1
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Exponents and nth roots
What is 2x
2x =2
12x x x 2
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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
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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)
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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
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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
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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
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