simple properties of exponents with multiplying and dividing

7/29/2019 Simple Properties of Exponents with Multiplying and Dividing

1/25

Simple Properties of Exponents

with Multiplying and Dividing

By L.D.


2/25

Problem 1

25 x 23


3/25

Problem 1

25 x 23

Most might say the answer is 415.What the problem reallylooks like is this though, is this;

25 = 2 x 2 x 2 x 2 x 2

23 = 2 x 2 x 2

So since we have eight twos and an exponent shows howmany times your base number (2) is multiplied our answer is28. You can multiply it now, I will use a calculator and I got 2 x2 x 2 x 2 x 2x 2 x 2 x 2 = 256. Most teachers will just let youleave it at 28.


4/25

Problem 1

25 x 23

Another way to get your answer is just to add

the exponents. You will get the same answer as

if you did it the other way though, 28.


5/25


6/25

Example Problems

1. z3 x z4 x z6

2. 4 x 42 x 42

3. 38

x 32


7/25

Example Problems

1. z3 x z4 x z6

2. 4 x 42 x 42

3. 38

x 32

1. z13

2. 45

3. 310


8/25

Problem 2

1. (25)3


9/25

Problem 2

1. (55)3

This one is a bit different from the last ones, you

are multiplying the already there exponents, so

it is basically (5 x 5 x 5 x 5 x 5) multiplied by

three, making your answer (5 x 5 x 5 x 5 x 5 x 5 x

5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5) or 515.


10/25

Example Problems

1. (w6)2

2. ((-26)2)3

3. (5)4


11/25

Example Problems

1. (w6)2

2. ((-26)2)3

3. (5)4

1. w12

2. (-2)36

3. 54


12/25

Mini Lesson

When you get a problem like (-

23)4, instead of it being -212, itwill always be (-2)12


13/25

Problem 3

1. 23 2


14/25

Problem 3

1. 23 2

Now, like the first one we have to put it into anatural form.

(2 x 2 x 2) 2

Since we are taking away one of the twos wehave 22 leftover.


15/25

Problem 3

1. 23 2

The simple way to do this is to minus theexponents, you will get 22.


16/25

Example Problems

1. 45 44

2. (-4)2 (-4)

3. 32

3


17/25

Example Problems

1. 45 44

2. (-4)2 (-4)

3. 3

3

3

1. 4

2. (-4)

3. 3

2


18/25

Problem 4

1. (2cy4)3


19/25

Problem 4

1. (2cy4)3

Now, we need to remember that the probleminside is actually 2 x c x y4 so when we are

bringing the exponent in it turns into;

23c3y12


20/25

Example Problems

1. (2z15)2

2. (27c2z4)3

3. (2cysfdfgfg)3


21/25

Example Problems

1. (2z15)2

2. (27c2z4)3

3. (2cysfdfgfg)3

1. 22z30

2. 221c6z12

3. The answer is not

23c3y3s3f3d3f3g3f3g3 but

rather it is 23c3y3s3f9d3g6

since we combine the ones

that have the same basetogether.


22/25

Problem 5

1. (2y7/y5)5


23/25

Problem 5

1. (2y7/y5)5

To get our answer we go through two steps. Firstwe distribute to get 25y35/y25, then we go to our

next step and divide to get 25y10.


24/25

Example Problems

1. (3/8)5 (35/85)

2. (2y7/y5)3

3. y

4

x (3c

3

y)

2

4. 5w/5w


25/25

Example Problems

1. (35/85) (3/8)5

2. 2. (2y7/y5)3

3. y

4

x (3c

3

y)

2

4. 5w/5w

1. 1

2. 23y6

3. 3

2

c

6

y

6

4. 1

simple properties of exponents with multiplying and dividing

Documents