Need help on simplifing some problems...please

[Guest]

My daughter has music engagement today so didn't have math class..She did these last night and asked me to look them over? So far she's got what I got but that doesn't reassure me. so here I am...
Simplifiy these problems- I have her answers but not sure if they are in the right direction???

1. 6ab^-4/2 a^-2b^2 = she got 3 and a^2/b^6

2. Squre root of x^3(sqrtx^5) I'm not sure how to write this the x^3 is under 1 square foot sign but the x^5 is under one of it's own and the one x^3 is also under...

We came up with X^5/6


3. Which one of the follwing is a solution to x^2 -8x + 13 = 0 I got E
a. 5.732
b. -2.2683
c. 4 - (sqrt) 3
d. 4 + i (sqrt) 3
e. no of these


4.Solve x^2 +6 < or equal to 5x She has (2,3)

Thanks for any body out there that can help!!! :wink:

 

[stapel]

1. 6ab^-4/2 a^-2b^2 = she got 3 and a^2/b^6

She got two answers, "3" and "a²/b⁶"...? Please reply with all of her steps.

2. Squre root of x^3(sqrtx^5) I'm not sure how to write this the x^3 is under 1 square foot sign but the x^5 is under one of it's own and the one x^3 is also under...

"Is also under" what? Please clarify.

We came up with X^5/6

Is "X" the same as "x"? Is this "x⁵/6" or "x^5/6" or something else? Were the instructions to "simplify", to "express using rational exponents", or something else? Please clarify.

3. Which one of the follwing is a solution to x^2 -8x + 13 = 0 I got E

Please reply showing your work and the solution you obtained, which induced you to conclude that none of the posted answers was valid.

4.Solve x^2 +6 < 5x; She has (2,3)

Close. Note that the "or equal to" means that the interval endpoints are included.

Eliz.

 

[Guest]

hope this cleans them up some! H

1. the answer is 3a^-2/a

Sorry I made it harder than it needed to be!

2.I don't know how to write this the first square root sing is over both x^3 and Sqare root x^5 but the x^5 is under a second sqare root sign? Is that any clearer...I hope so!

3. the correct answer is A i can see here in her work where she messed up...she forgot to sqare the first term!

4. I don't know the difference bet ween using () or [] and we culdn't find it in her book so she thought b but I thought it was a????

 

[stapel]

1. the answer is 3a^-2/a

What happened to the "b" variable?

I'm not entirely clear on what the original exercise was, either. Using the formatted explained in "Karl's Notes", or any of the other links in the "Forum Help" pull-down menu at the very top of the page, would likely be very helpful.

2.I don't know how to write this the first square root sing is over both x^3 and Sqare root x^5 but the x^5 is under a second sqare root sign?

So the expression is as follows...?

. . . . .sqrt[ x³ sqrt[ x⁵ ] ]

And what are the instructions?

3. the correct answer is A i can see here in her work where she messed up...she forgot to sqare the first term!

Which "first term"? The first term written down in the usual formulation of the Quadratic Formula is not actually squared.

Also, do the instructions say to give the solution in rounded approximate form, rather than as an exact answer? If so, then the request to provide the "one" correct answer is unanswerable.

4. I don't know the difference bet ween using () or [] and we culdn't find it in her book so she thought b but I thought it was a????

You thought "it" was a... what?

If her book does not discuss interval notation, then this must be a topic that she was assumed already to know, having covered it in previous courses. You can learn about interval notation many places online, but, in general, the rule is that included endpoints are indicated by square brackets, while curly parentheses indicate an endpoint which is not included.

Eliz.

 

[Guest]

try to clearifay again

on problem 1. the answer we have is3a^3/b^6



2. yes ...it just says simplify .sqrt[ x3 sqrt[ x5 ] ] and the answer choices are:

a. X^4/5
b. X^4/3
c. X^5/6
d. X^13/6
e. none of these

The other ones you answered when you told me about the different brackets...
Thanks sorry number 2 has been hard for me to write but I used in Karl's help!

 

[soroban]

Hello, 4 little piggies mom!

It would help if you used more parentheses.

1. 6ab^-4/2 a^-2b^2 = she got 3 and a^2/b^6

I'm guessing . . .

I think you meant: [6ab^{-4}] / [2a^{-2}b^2]

We have: \(\displaystyle \L\,\frac{6\cdot a\cdot b^{^{-4}}}{2\cdot a^{^{-2}}\cdot b^{^2}}\)

I would "move" the factors with negative exponents: \(\displaystyle \L\,\frac{6\cdot a\cdot a^2}{2\cdot b^2\cdot b^4}\)

Then simplify: \(\displaystyle \L\,\frac{3a^3}{b^6}\)

2. Squre root of x^3(sqrtx^5)
I'm not sure how to write this the x^3 is under 1 square root sign
but the x^5 is under one of it's own and the one x^3 is also under.
We came up with X^5/6

Next time try: sqrt[x^3 sqrt(x^5)]

We have: \(\displaystyle \L\,\sqrt{x^3\sqrt{x^5}}\;=\;\sqrt{x^3\cdot x^{\frac{5}{2}}} \;= \;\sqrt{x^{\frac{11}{2}}} \;= \;\left(x^{\frac{11}{2}}\right)^{\frac{1}{2}}\;=\;x^{\frac{11}{4}}\)

3. Which one of the follwing is a solution to: \(\displaystyle \,x^2\,-\,8x\,+\,13\:=\:0\)

\(\displaystyle a.\;5.732\;\;\;b)\;-2.2683\;\;\;c.\;4\,-\,\sqrt{3}\;\;\;d.\;4\,+\,i\sqrt{3}\;\;\;e.\;\text{none of these}\)

We have a quadratic equation with: \(\displaystyle \,a\,=\,1,\;b\,=\,-8,\;c\,=\,13\)

Quadratic Formula: \(\displaystyle \L\,x\;=\;\frac{-(-8)\,\pm\,\sqrt{(-8)^2\,-\,4(1)(13)}}{2(1)} \;=\;\frac{8\,\pm\,\sqrt{12}}{2}\;=\;\frac{8\,\pm\,2\sqrt{3}}{2}\)

The roots are: \(\displaystyle \,x\;=\;4\,\pm\sqrt{3}\,\) . . . or \(\displaystyle \,5.732050808\) and \(\displaystyle 2.267949192\)

The answer choices are sneaky!
Answer (a) is close, but only an approximation.
Answer (b) is also close, but wrong.
Answer (d) is wrong.
Answer (c) is one of our answers . . . THAT is the choice.

4.Solve \(\displaystyle \,x^2\,+\,6\;\leq\;5x\;\;\;\)She has \(\displaystyle (2,3)\).

Pretty good . . .
But it said "less than or equal to" . . . she should include the endpoints: \(\displaystyle [2,\,3]\)