# Thread: What does this mean?

1. ## What does this mean?

What expression raised to the fourth power is -8x^6y^9z^15

2. Originally Posted by clueless82
What expression raised to the fourth power is -8x^6y^9z^15
you want to find an expression so that $\displaystyle (\mbox{the expression})^4 = -8x^6y^9z^{15}$ that is, $\displaystyle \mbox{the expression } = \pm \sqrt[4]{-8x^6y^9z^{15}}$

3. ## The problem in the book above it

says... What expression raised to the third is -8x^6y^9z^15? and the books answer in the back is y^3-y+6

I have No idea how they got that and there is no examples about it...

4. Originally Posted by clueless82
says... What expression raised to the third is -8x^6y^9z^15? and the books answer in the back is y^3-y+6

I have No idea how they got that and there is no examples about it...
is it to the third or to the fourth. secondly, there is no way that answer is right. you are looking at the wrong problem in the answer section.

5. Originally Posted by clueless82
says... What expression raised to the third is -8x^6y^9z^15? and the books answer in the back is y^3-y+6

I have No idea how they got that and there is no examples about it...
Well, the book is wrong

Let L denote our quantity

So we have that

$\displaystyle L^3=-8x^6y^9z^5\Rightarrow{L=\sqrt[3]{-8x^6y^9z^15}=-2x^2y^3z^5}$

Just think about it, how does one take the $\displaystyle \sqrt[n]{}$ of a monomial and get a trinomial?

6. Originally Posted by clueless82
says... What expression raised to the third is -8x^6y^9z^15? and the books answer in the back is y^3-y+6

I have No idea how they got that and there is no examples about it...
Well....we want to find $\displaystyle \varphi$ (our expression)

If $\displaystyle \varphi^3=-8x^6y^9z^{15}$ then $\displaystyle \varphi=\sqrt [3] {-8x^6y^9z^{15}}\implies\varphi=-2x^2y^3z^5$.

This is not $\displaystyle y^3-y+6$...are you sure that this was the answer?

7. ## Thank You All So Very Much!!

I am clueless with algebra.. have failed every class i have taken with it... even after tutors and HOURS of studying and reading examples.. now I have 29 problems and only 3 and 1/2 hours to get them done! :+(
thanks again all! I admire YOU ALL!!

8. Originally Posted by clueless82
I am clueless with algebra.. have failed every class i have taken with it... even after tutors and HOURS of studying and reading examples.. now I have 29 problems and only 3 and 1/2 hours to get them done! :+(
thanks again all! I admire YOU ALL!!
do you understand what happened here? how did they go from the expression with the cube-root to the final answer?