Exponents and nth roots inverse operations. Exponents and nth roots What is (y 2 )(y 5 )? It is...

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