Help with 2 math questions please?

Question

lemanual · Answer

lemanual · Answer

mathstudent55 · Answer

In the first problem, each choice has a multiplication of two quantities.
First, multiply the numbers together.
For example, in A:
$\large 6a^5(6a^5) = 6 \times 6 \times a^5 \times a^5$

mathstudent55 · Answer

First, multiply $6 \times 6$
What is that equal to?

lemanual · Answer

36

mathstudent55 · Answer

Good.
Now you need to multiply $\large a^5 \times a^5$

lemanual · Answer

a^10x?

lemanual · Answer

or 25

mathstudent55 · Answer

To multiply powers with the same base, write the base and ADD the exponents.

For example, $\large b^5 \times b^7 = b^{5 + 7} = b^{12} $

mathstudent55 · Answer

Now try it with 

$\large a^5 \times a^5$

lemanual · Answer

a10

mathstudent55 · Answer

Correct.
That means that 

$\large 6a^5 (6a^5) = 36a^{10} $

Is that the solution in choice A?

lemanual · Answer

ohhh so first and second?

lemanual · Answer

This? http://prntscr.com/dfp3v5

mathmale · Answer

Please use the symbol ^ to indicate exponentiation.

correct:  c^5
incorrect:  c5

lemanual · Answer

O_O Yes sir

mathstudent55 · Answer

Part of learning math (or anything else) is to pay attention.
I just showed you what the correct answer to the problem in part A is.
Now compare our correct answer with the answer in part A of your problem.
Are the answers the same?

mathstudent55 · Answer

We worked together and correctly on part A and got this.

$\large 6a^5 (6a^5) = 36a^{10}$

The problem has this:

$\large 6a^5 (6a^5) = 36a^{25}$

We did our solution correctly following the rules of multiplying powers.
Since the problem has a different solution, and our solution is correct, the conclusion must be that part A of the problem is incorrect.
We can even tell what their mistake is.
They multiplied the exponents of variable a, when they should have added them.

lemanual · Answer

No so it's only the second one? cause you said add the exponents right? cause 6a^5+(6a^5)= 6x6=36 so thats correct but the exponent 5 you have to add and it says 25 which it isn't right?

mathstudent55 · Answer

Remember, the questions asks which of the 4 parts were done CORRECTLY.
Part A is not one of them.

lemanual · Answer

So do I multiply the exponents also?

mathstudent55 · Answer

Have you read anything I wrote above?

lemanual · Answer

Yes I said you told me to add them but are you saying the first option is correct? cause if so how

lemanual · Answer

to add the exponents

mathstudent55 · Answer

I just wrote this above:

Remember, the questions asks which of the 4 parts were done CORRECTLY.
Part A is not one of them.

lemanual · Answer

I added them and it's 5+5 which = 10 so that means it isn't first option

mathstudent55 · Answer

Adding the exponents was correct for part A.
We were correct.
The problem is incorrect.

lemanual · Answer

Because it says 36a^25

mathstudent55 · Answer

You are correct now.
Option A is incorrect.

lemanual · Answer

Yeah so second option cause all of what I added was correct

mathstudent55 · Answer

Option A of the problem, INCORRECTLY multiplied the powers when it should have added them.

lemanual · Answer

yeah I know so It's only second option correct?

mathstudent55 · Answer

$\large 5x^4(4x^2) = 5 \times 4 \times x^4 \times x^2 = 20x^6$

You are correct. Part B is correct.

mathstudent55 · Answer

Now let's look at C.

mathstudent55 · Answer

Here the numbers are positive and negative.
What do you get when you multiply a positive number by a negative number?

lemanual · Answer

Positive number

mathstudent55 · Answer

$\large 6b^4(-3b^4) = 6 \times (-3) \times b^4 \times b^4$

What is 6 * (-3) = ?

lemanual · Answer

-18

mathstudent55 · Answer

No.

Rule for multiplying signed numbers:
positive * positive = positive
negative * negative = positive
positive * negative = negative
negative * positive = negative

lemanual · Answer

ohh

mathstudent55 · Answer

Quick way of stating the rule:
If you multiply two numbers with the same sign, the answer is positive.
If you multiply two numbers with different signs, the answer is negative.

mathstudent55 · Answer

Ok?

lemanual · Answer

Yes

mathstudent55 · Answer

Good.
Back to C.

$\large 6b^4(-3b^4) = 6 \times (-3) \times b^4 \times b^4$

Keep the rule above in mind.

What is 6 * (-3) = ?

mathstudent55 · Answer

6 is positive. -3 is negative.
The numbers have different signs, so answer is? (positive or negative)

lemanual · Answer

Negative?

mathstudent55 · Answer

Correct.
What is 6 * 3?

lemanual · Answer

18

mathstudent55 · Answer

Since 6 * 3 = 18, then 
6 * (-3) = -18
Ok?

lemanual · Answer

I said -18 .-.

mathstudent55 · Answer

Oh. I didn't see that.
You did write positive above, and I was responding to that.

mathstudent55 · Answer

Ok, so now we have -18.
What is $b^4 \times b^4$ ?

lemanual · Answer

8

mathstudent55 · Answer

To multiply powers with the same base, we write the same base and ADD exponents.

mathstudent55 · Answer

The exponent is 8.

$\large 6b^4(-3b^4) = 6 \times (-3) \times b^4 \times b^4 = -18b^8$

mathstudent55 · Answer

Is that the solution given in part C?

lemanual · Answer

Yes

mathstudent55 · Answer

Good.
Choose C also.
Now you can do part D.
What do you get for the product?

lemanual · Answer

I checked D and It's right because they added the exponent and got 9... 7+2=9 then 3*4 =12 and the answer is 12^9

lemanual · Answer

well 12z^9

mathstudent55 · Answer

Excellent.
You got the hang of this now.
Good work!

lemanual · Answer

Yeah :D because of you :) ty

mathstudent55 · Answer

Answer to the first problem, then, is B, C, D.

mathstudent55 · Answer

Are you ready for the second problem now?

lemanual · Answer

Yes

mathstudent55 · Answer

Ok.
The second problem uses the first one as a building block.
In the second problem, you need to use the distributive property in each part first.
Once you have used the distributive property, then you multiply terms like we did in the first part.

mathstudent55 · Answer

Are you familiar with the distributive property?

lemanual · Answer

I checked the first Option A and it's wrong :D

lemanual · Answer

should be 6 instead of 8 right?

mathstudent55 · Answer

Here it is:

The distributive property of multiplication over addition

$a(b + c) = ab + ac$

lemanual · Answer

ohh yeah I know that

lemanual · Answer

I got the hang of it now :D can I do the rest and you just tell me if it's correct :))

mathstudent55 · Answer

Now let's look at part A.

$\large -6y^4(4y^2 + 2)$

The first step is to apply the distributive property:

$\large -6y^4(4y^2 + 2) = -6y^4(4y^2) +~(- 6)y^4(2) =$

Now we do each multiplication as we did for the first problem.

$\large = -24y^6 = 12y^4$

You are correct.
It is an exponent of 6, not 8.

mathstudent55 · Answer

You learned well.
Good job.

lemanual · Answer

http://prntscr.com/dfpkib ty so much I understand it now :)

lemanual · Answer

I am having trouble with this one though if you don't mind http://prntscr.com/dfpl9d

mathstudent55 · Answer

Correct.
Once again, great job!

lemanual · Answer

Because of you :) and ty

lemanual · Answer

Are you there?

mathstudent55 · Answer

You're welcome.

lemanual · Answer

nvm it was A :D

lemanual · Answer

for this one http://prntscr.com/dfpl9d

lemanual · Answer

Bye :) learn something new every day