Uploaded by videosbyjulieharland on 20.11.2009

Transcript:

>> Okay, we're going to simplify these exponents.

So we have 2N squared.

Remember, that's 2N times 2N, so that's going

to be 4N squared times negative 4N cubed.

Now, we do 4 times negative 4 is negative 16.

And N squared times N cubed, you have to add the exponents,

unless you want to write it all out and count them up.

You'll get N to the 5th.

So that's negative 16N to the 5th.

All right, let's do this next one.

Now, 10 over 2 is regular canceling 10 over 2 cancels.

You get a 5.

I have an M to the 7th over M to the 1st.

So what's going to happen here is I'll have the 5

in the numerator.

Now we'll deal with the Ms.

There's more on the top,

so you do 7 minus 1 to get M to the 6th.

Now, look at the next one.

You have a C to the 5th in the bottom.

There's more Cs in the bottom.

So we'll do 5 minus 2 and be left with C cubed in the bottom.

And the X to the 8th completely cancel out.

So that's our answer.

All right, we've got a negative number raised to the 4th.

So a negative raised to an even exponent means you're going

to have a positive answer

because you'll have four negative signs.

So I'm going to have a negative 2 to the 4th, which is the same

as 2 to the 4th, so I'll have 2 to the 4th really.

And I'm going to have an X cubed to the 4th and a 3 to the 4th,

and an N 4th to the 4th.

If you want, you could think of that

as a negative 2 to the 4th, okay?

We get the same answer.

So that's 2 times 2 times 2 times 2.

We know four negatives is going to make a positive 16.

We're going to multiply exponents, X to the 12th.

3 to the 4th is 3 times 3 times 3 times 3, which is 81.

And N to the 4th to the 4th power, also we're going

to multiply exponents, okay?

All right, let's go on to Part D. You've got negative 5

to the 3rd power.

So we're going to have a negative 5 to the 3rd power.

You have an X squared to the 3rd power, a 3 to the 3rd power

and an N to the 3rd power.

All right, so this time, it's going to be negative,

when you have three negative signs.

So 5 times 5 times 5 is 125.

So I'm going to write my answer with a minus sign out in front,

125, multiply exponents here, X to the 6th.

3 cubed is 3 times 3 times 3, N cubed.

Just so it's easier to read this, I'm going to change colors

and move it down a little bit.

And there you go.

All right, let's look at E. Well, here we're dealing

with some negative exponents.

So we're going to take anything that has a negative exponent

and switch it from numerator to denominator, vice versa.

Now, you can't do that with the numbers.

The 2 and the negative 5 are not exponents.

They stay as they are.

But this X to the negative 2 comes

down as an X to the positive 2.

And the M to the negative 3 comes down as a positive 3.

This X to the 4th is positive, so leave it alone.

It's already positive.

And the M to the negative 2 goes up.

So what I've done is taken the ones that have negatives,

I've taken those with the negative exponents,

and I've put them down here to make them positive.

You can see it right there by switching.

Okay, so we have this minus sign out front.

So we add the 2 and the 5.

And now what do we do?

Well, we have an X squared times an X to the 4th.

That's an X to the 6th.

And I have more Ms in the denominator.

So if I subtract 3 minus 1, I just have M to the 1st.

So I can leave it like that.

Now, you could put the negative 2 in the numerator

or put the minus sign out in front like I've done here.

All right, next one, F. What I could do here is simply

multiply-- raise everything to the negative 3 power first,

or I could fool around with all the negative signs

in the inside of the parentheses.

There are a few different ways to do this problem.

I'm going to go ahead and just write it as 3 to the negative 3.

Now, when I do an X to the negative 4 to the negative 3,

we'll multiply exponents, which we have X to the 12th.

And M squared to the negative 3

when I multiply exponents will be M to the negative 6th.

Now, again, I could take these ones

with the negative exponents,

and I know those go in the denominator.

So that's going to give you X to the 12th stays up at the top.

And then we have 3 cubed over M to the 6th.

So the last thing to do is simplify this 3 cubed,

so I get X to the 12th over 27 M to the 6th.

All right, accurately graph a line passing through 1,

negative 2, and have a slope of negative 3.

Well, here we are.

We know it goes through 1, negative 2.

So find that point and just put it down there.

There's 1, negative 2.

The slope is negative 3.

So you have to write that as negative 3 over positive 1.

You know the slope is going to be slanting

in that direction, if it's negative.

So in the X direction, I'm going positive 1, and then down 3,

where we get another point.

Now, the other way to write it is a positive 3

over a negative 1.

If you do that, you would say I'm going

from this point negative 1 and up three.

But in both cases, I'm going

to get slanting the correct direction.

And then we just go ahead

and draw hopefully a more accurate line than I have.

I can't use a ruler on what I'm using.

Okay, so then you want to write it in slope intercept form.

Okay, there's a couple ways to do this.

You could use the slope-point formula,

Y minus Y1 equals M times X minus X1, or you could look

at the picture and decide what B is.

And I could see B as going through 1 here.

Notice, I told you B is 1.

So one way of getting it is you just look at the picture.

You get Y equals-- you know the slope is negative 3, right?

X plus 1. So it looks

like that's what the answer should be.

And if you plug in this ordered pair, putting in 1 for X

and negative 2 for Y, it is a true equation.

So that does work.

But the other way to do it, instead of visualizing it,

is plugging in the numbers, the Y when you're plugging

in negative 2, the slope you're plugging in 3, and for X,

you're plugging in 1.

And you should get the same answer doing it this way.

Negative 3X plus 3.

And then subtract 1 from both sides.

You get negative 3X plus 1.

So we get the right equation, either by looking at the picture

or by using the slope-point formula.

So we have 2N squared.

Remember, that's 2N times 2N, so that's going

to be 4N squared times negative 4N cubed.

Now, we do 4 times negative 4 is negative 16.

And N squared times N cubed, you have to add the exponents,

unless you want to write it all out and count them up.

You'll get N to the 5th.

So that's negative 16N to the 5th.

All right, let's do this next one.

Now, 10 over 2 is regular canceling 10 over 2 cancels.

You get a 5.

I have an M to the 7th over M to the 1st.

So what's going to happen here is I'll have the 5

in the numerator.

Now we'll deal with the Ms.

There's more on the top,

so you do 7 minus 1 to get M to the 6th.

Now, look at the next one.

You have a C to the 5th in the bottom.

There's more Cs in the bottom.

So we'll do 5 minus 2 and be left with C cubed in the bottom.

And the X to the 8th completely cancel out.

So that's our answer.

All right, we've got a negative number raised to the 4th.

So a negative raised to an even exponent means you're going

to have a positive answer

because you'll have four negative signs.

So I'm going to have a negative 2 to the 4th, which is the same

as 2 to the 4th, so I'll have 2 to the 4th really.

And I'm going to have an X cubed to the 4th and a 3 to the 4th,

and an N 4th to the 4th.

If you want, you could think of that

as a negative 2 to the 4th, okay?

We get the same answer.

So that's 2 times 2 times 2 times 2.

We know four negatives is going to make a positive 16.

We're going to multiply exponents, X to the 12th.

3 to the 4th is 3 times 3 times 3 times 3, which is 81.

And N to the 4th to the 4th power, also we're going

to multiply exponents, okay?

All right, let's go on to Part D. You've got negative 5

to the 3rd power.

So we're going to have a negative 5 to the 3rd power.

You have an X squared to the 3rd power, a 3 to the 3rd power

and an N to the 3rd power.

All right, so this time, it's going to be negative,

when you have three negative signs.

So 5 times 5 times 5 is 125.

So I'm going to write my answer with a minus sign out in front,

125, multiply exponents here, X to the 6th.

3 cubed is 3 times 3 times 3, N cubed.

Just so it's easier to read this, I'm going to change colors

and move it down a little bit.

And there you go.

All right, let's look at E. Well, here we're dealing

with some negative exponents.

So we're going to take anything that has a negative exponent

and switch it from numerator to denominator, vice versa.

Now, you can't do that with the numbers.

The 2 and the negative 5 are not exponents.

They stay as they are.

But this X to the negative 2 comes

down as an X to the positive 2.

And the M to the negative 3 comes down as a positive 3.

This X to the 4th is positive, so leave it alone.

It's already positive.

And the M to the negative 2 goes up.

So what I've done is taken the ones that have negatives,

I've taken those with the negative exponents,

and I've put them down here to make them positive.

You can see it right there by switching.

Okay, so we have this minus sign out front.

So we add the 2 and the 5.

And now what do we do?

Well, we have an X squared times an X to the 4th.

That's an X to the 6th.

And I have more Ms in the denominator.

So if I subtract 3 minus 1, I just have M to the 1st.

So I can leave it like that.

Now, you could put the negative 2 in the numerator

or put the minus sign out in front like I've done here.

All right, next one, F. What I could do here is simply

multiply-- raise everything to the negative 3 power first,

or I could fool around with all the negative signs

in the inside of the parentheses.

There are a few different ways to do this problem.

I'm going to go ahead and just write it as 3 to the negative 3.

Now, when I do an X to the negative 4 to the negative 3,

we'll multiply exponents, which we have X to the 12th.

And M squared to the negative 3

when I multiply exponents will be M to the negative 6th.

Now, again, I could take these ones

with the negative exponents,

and I know those go in the denominator.

So that's going to give you X to the 12th stays up at the top.

And then we have 3 cubed over M to the 6th.

So the last thing to do is simplify this 3 cubed,

so I get X to the 12th over 27 M to the 6th.

All right, accurately graph a line passing through 1,

negative 2, and have a slope of negative 3.

Well, here we are.

We know it goes through 1, negative 2.

So find that point and just put it down there.

There's 1, negative 2.

The slope is negative 3.

So you have to write that as negative 3 over positive 1.

You know the slope is going to be slanting

in that direction, if it's negative.

So in the X direction, I'm going positive 1, and then down 3,

where we get another point.

Now, the other way to write it is a positive 3

over a negative 1.

If you do that, you would say I'm going

from this point negative 1 and up three.

But in both cases, I'm going

to get slanting the correct direction.

And then we just go ahead

and draw hopefully a more accurate line than I have.

I can't use a ruler on what I'm using.

Okay, so then you want to write it in slope intercept form.

Okay, there's a couple ways to do this.

You could use the slope-point formula,

Y minus Y1 equals M times X minus X1, or you could look

at the picture and decide what B is.

And I could see B as going through 1 here.

Notice, I told you B is 1.

So one way of getting it is you just look at the picture.

You get Y equals-- you know the slope is negative 3, right?

X plus 1. So it looks

like that's what the answer should be.

And if you plug in this ordered pair, putting in 1 for X

and negative 2 for Y, it is a true equation.

So that does work.

But the other way to do it, instead of visualizing it,

is plugging in the numbers, the Y when you're plugging

in negative 2, the slope you're plugging in 3, and for X,

you're plugging in 1.

And you should get the same answer doing it this way.

Negative 3X plus 3.

And then subtract 1 from both sides.

You get negative 3X plus 1.

So we get the right equation, either by looking at the picture

or by using the slope-point formula.