Alegbra 3 Review Help during trig.

[shooterman]

Questions says "Simplify by performin the indicated operations"

On this type of problem i didn't know really where to start because i don't remember dealing with cubed exponens.
--1/3---------------2/3------------1/3 <------------------------------------------------Exponent
(x---- Minus 2)(x-------"Plus" 2x ----"plus"+4)

Well my math teacher help me with the other work but the other problems didn't have a cubed root as exponent.

Thanks for the Help :mrgreen:

Thanks to Mark this is the proper way i am supposed to type the math problem

[x^(1/3) - 2]*[x^(2/3) + 2x^(1/3) + 4]

 

[mmm4444bot]

Hi shooterman:

We cannot use repeated spaces or hyphens at this web site to "draw" stuff because this web site strips out repeated spaces and does not use a fixed-width font to display posts. (As you can see from your post, the result is garbage.)

If you really want to "draw" stuff, then you'll need to learn about the BBCode tags that force a fixed-width font. It's probably easier for you to simply learn the basics of typing standard math notation.

Go HERE to learn more about how to properly type math, using a keyboard.

When typing math expressions, we use the caret symbol (^ is shift-6, on most keyboards) to denote exponents.

Use parentheses and square brackets to group things together. If you don't properly use grouping symbols, then people often need to guess what belongs in denominators of fractions or what belongs in the exponent position. (In math, guessing is generally not good.)

Does your exercise look like the following?

\(\displaystyle (x^{1/3} - 2)(x^{2/3} + 2x^{1/3} + 4)\)

If not, then I've guessed wrongly.

If so, then we type it using grouping symbols and the caret symbol as follows.

[x^(1/3) - 2]*[x^(2/3) + 2x^(1/3) + 4]

NEXT, do you understand the Distributive Property?

A*(B + C) = A*B + A*C

To carry out the indicated multiplication, in your exercise as I've interpreted it, we need to use the Distributive Property twice.

We need to multiply each of the three terms inside the second factor by each of the two terms in the first factor.

In other words, you will need to do all of the following multiplications, followed by adding the resulting products.

x^(1/3) * x^(2/3) = ?

x^(1/3) * 2x^(1/3) = ?

x^(1/3) * 4 = ?

-2 * x^(2/3) = ?

-2 * 2x^(1/3) = ?

-2 * 4 = ?

NEXT, have you learned the basic properties of exponents?

You need to know the following property of exponents, in order to multiply the powers above together.

x^n * x^m = x^(n + m)

In other words, when two powers of x are multiplied together, we add the exponents.

The fact that the given exercise contains cube roots should not throw you off track because the simplification proceeds the same way regardless of having exponents 1/2, 1/3, 1/4, or any other.

Please show us what you get, after you complete the six multiplications above and combine like-terms.

Cheers,

~ Mark

 

[shooterman]

Thanks Mark i will change the post to properly type the problem also do what you ask.
oh when you mean adding the exponents do you mean this
x^1/3 + x^ 1/3 equals x^2/3?

 

[mmm4444bot]

oh when you mean adding the exponents do you mean this
x^1/3 + x^ 1/3 equals x^2/3?

Yes, but we only add exponents when powers are multiplied.

In your example above, you typed the addition of two powers, instead.

You also did not put grouping symbols around the exponents.

x^(1/3) + x^(1/3) = 2x^(1/3)

x^(1/3) * x^(1/3) = x^(1/3 + 1/3) = x^(2/3)

 

[shooterman]

oh okay i will fix that

 

[shooterman]

Well this is what i got

x^(1/3) * x^(2/3) = 2x^(3/3)< what will ^(3/3) do to this part 2x^(3/3)<

x^(1/3) * 2x^(1/3) =2x^(2/3)

x^(1/3) * 4 = 4x^(2/3)

-2 * x^(2/3) = -2x^(2/3)

-2 * 2x^(1/3) = -4x^(1/3)

-2 * 4 = -8

 

[mmm4444bot]

Well this is what i got

x^(1/3) * x^(2/3) = 2x^(3/3) Incorrect. There's no factor of 2 in this multiplication. Also, ask yourself "What does 3/3 equal?"

x^(1/3) * 2x^(1/3) =2x^(2/3) Correct.

x^(1/3) * 4 = 4x^(2/3) Incorrect. How did you get 2/3?

-2 * x^(2/3) = -2x^(2/3) Correct.

-2 * 2x^(1/3) = -4x^(1/3) Correct.

-2 * 4 = -8 Correct.

 

[shooterman]

Re:

Well this is what i got

x^(1/3) * x^(2/3) = 2x^(3/3) Wrong. There's no factor of 2. Also, ask yourself "What does 3/3 equal?" Correction x^(3/3) What does 3/3 equal? does it cancel the exponent?

x^(1/3) * 2x^(1/3) =2x^(2/3) Correct.

x^(1/3) * 4 = 4x^(2/3) Wrong. How did you get 2/3? Correction 4x^(3/3)

-2 * x^(2/3) = -2x^(2/3) Correct.

-2 * 2x^(1/3) = -4x^(1/3) Correct.

-2 * 4 = -8 Correct.

 

[Deleted member 4993]

Re: Re:

Well this is what i got

x^(1/3) * x^(2/3) = 2x^(3/3) Wrong. There's no factor of 2. Also, ask yourself "What does 3/3 equal?" Correction x^(3/3) What does 3/3 = 1 equal? must have learnt it in second grade!!

does it cancel the exponent?

x^(1/3) * 2x^(1/3) =2x^(2/3) Correct.

x^(1/3) * 4 = 4x^(2/3) Wrong. How did you get 2/3? Correction 4x^(3/3)

-2 * x^(2/3) = -2x^(2/3) Correct.

-2 * 2x^(1/3) = -4x^(1/3) Correct.

-2 * 4 = -8 Correct.

 

[mmm4444bot]

What does 3/3 equal?

Any Real number (other than zero) divided by itself equals 1.

'

x^(1/3) * 4 = 4x^(3/3)

This is still incorrect. (You might need to take algebra again, before attempting to learn trigonometry.)

 

[shooterman]

Re:

What does 3/3 equal?

Any Real number (other than zero) divided by itself equals 1.
I know that.
'

x^(1/3) * 4 = 4x^(3/3)

This is still incorrect. (You might need to take algebra again, before attempting to learn trigonometry.)

so does the 1from the 3/3 in this 4x^(3/3) will make it 5x
want to know where one goes

 

[mmm4444bot]

4x^(3/3) = 4x^1 = 4x

Did anybody teach you what exponents mean? How old are you? How long has it been since you studied algebra?

 

[Deleted member 4993]

Re: Re:

What does 3/3 equal?

Any Real number (other than zero) divided by itself equals 1.
I know that.
'

x^(1/3) * 4 = 4x^(3/3)

This is still incorrect. (You might need to take algebra again, before attempting to learn trigonometry.)

so does the 1from the 3/3 in this 4x^(3/3) will make it 5x
want to know where one goes

\(\displaystyle 2^1 \, = \, 2\)

\(\displaystyle 9^1 \, = \, 9\)

\(\displaystyle x^1 \, = \, x\)

 

[shooterman]

well thx

Exponent is the number how many times the number or base to be used in multiplying.

Just finished Algebra 3 just forgot what to do with ^(3/3) exponent
:roll:

 

[mmm4444bot]

Since you understand exponentiation, please explain why you're thinking that an exponent of 1 would cause the coefficient on x to increase by 1.

You were thinking that 4x^1 means 5x.

This is obviously wrong, but I need to know why you don't recognize that it's wrong.

 

[shooterman]

k so i get
6x + -4x^(1/3) -8 correct?
Is that simplied or there is more

Why i thought that well i don't know must of forgotten

 

[mmm4444bot]

Your answer is not even close!

Show me again the six products that you get after applying the distributive property twice.

 

[shooterman]

2x
2x^(2/3)
4x
-2x^(2/3)
-4x^(1/4)
-8

 

[mmm4444bot]

Incorrect: 2x
Correct: 2x^(2/3)
Incorrect: 4x
Correct: -2x^(2/3)
Incorrect: -4x^(1/4)
Correct: -8

You are not ready to attempt exercises like this one.

I cannot help you further because you are not ready. (This forum is not an online classroom; we're here for students who have basic comprehension of foundational concepts.)

I will finish my contributions to this thread by giving you the answer.

\(\displaystyle (x^{1/3} - 2)(x^{2/3} + 2x^{1/3} + 4) = x + 2x^{2/3} + 4x^{1/3} - 2x^{2/3} - 4x^{1/3} - 8 = x - 8\)

Feel free to ask specific questions; perhaps, somebody else here can help you.

 

[Mrspi]

well thx

Exponent is the number how many times the number or base to be used in multiplying.

Just finished Algebra 3 just forgot what to do with ^(3/3) exponent
:roll:

I'm sorry...Algebra 3?????

You should have covered exponents, I think.

4 x[sup:3h44hpfv]3/3[/sup:3h44hpfv]

4 x[sup:3h44hpfv]1[/sup:3h44hpfv]

4x

We can do only so much here.