The first thing that we covered was Integer Powers of Negative Numbers:

- For the even powers the answer was a positive number

Ex:

= 81

-For the odd powers the answer was a negative number =9

Ex:

= -27

= -3

- And of course anything raised to the 0 is always 1:

We also worked with negative powers and saw how the answer varied if they were included:

- We found out that the same result happens with if the power is odd then you get a negative answer and if the power is even then it is a positive solution, but there is one twist you evaluate the problem from the denominator spot as you recall from chapter 7.

Ex:

Even Powers: Odd Powers:

Lets try:

Positive- = - alright positive radicals are ok. now lets try negative

Negative- - lets break it down = * * which is equal to i

*Remember- imaginary numbers = i

Now lets try the same sort of math multiplying * when x and y are positive and negative:

Ex:

Positive-

= -3

- And of course anything raised to the 0 is always 1:

= 1

We also worked with negative powers and saw how the answer varied if they were included:

- We found out that the same result happens with if the power is odd then you get a negative answer and if the power is even then it is a positive solution, but there is one twist you evaluate the problem from the denominator spot as you recall from chapter 7.

Ex:

Even Powers:

=

= =

=

The next concept of the lesson was the question was posed: Are there Noninteger powers of negative numbers?Lets try:

Positive- = - alright positive radicals are ok. now lets try negative

Negative- - lets break it down = * * which is equal to i

*Remember- imaginary numbers = i

Now lets try the same sort of math multiplying * when x and y are positive and negative:

Ex:

Positive-

*=

Negative-

Last we saw what happens when x is negative and n is even

We found that it is undefined you can see this on the graph with a parabola and there is a single horizontal line going through the y axis: this signifies 0 solutions or undefined-

If this still doesn't explain the concept well enough the summary on the back of the 8.7 notes does a great job on stating the conclusion to the certain problems are.

Negative-

* = 3i * 2i = 6which is -6

*Remember = -1 and so for example is basicallyand = i so it is 3i

Next we went over the fact that you are not allowed to do negative numbers raised to a fraction

ex-

*But we did figure out a easy was around this was to use- form

ex-

*Remember = -1 and so for example is basicallyand = i so it is 3i

Next we went over the fact that you are not allowed to do negative numbers raised to a fraction

ex-

- this problem is impossible because you end up with 2 different solutions, instead we just call this undefined.

*But we did figure out a easy was around this was to use- form

ex-

= -3

Then we asked ourselves what happened in form if x is negative and n is odd-

The answer is that you get one solution just how the problem above worked out-

= -3

The explanation to this is in the graph where there is a single horizontal line going through the y axis: this signifies 1 solution-

Then we asked ourselves what happened in form if x is negative and n is odd-

The answer is that you get one solution just how the problem above worked out-

= -3

The explanation to this is in the graph where there is a single horizontal line going through the y axis: this signifies 1 solution-

Last we saw what happens when x is negative and n is even

We found that it is undefined you can see this on the graph with a parabola and there is a single horizontal line going through the y axis: this signifies 0 solutions or undefined-

If this still doesn't explain the concept well enough the summary on the back of the 8.7 notes does a great job on stating the conclusion to the certain problems are.

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