SOLUTION: Good morning! An interesting radical conundrum for me: SIMPLIFY: fourth root of (9 / z^5) or (9 / z^5)^(1/4) I broke it down: (9)^(1/4) / (z^5)^(1/4) Then I mult

Algebra ->  Square-cubic-other-roots -> SOLUTION: Good morning! An interesting radical conundrum for me: SIMPLIFY: fourth root of (9 / z^5) or (9 / z^5)^(1/4) I broke it down: (9)^(1/4) / (z^5)^(1/4) Then I mult      Log On


   

Question 307135: Good morning!
An interesting radical conundrum for me:
SIMPLIFY: fourth root of (9 / z^5) or (9 / z^5)^(1/4)

I broke it down: (9)^(1/4) / (z^5)^(1/4)
Then I multiplied top and bottom by (z^5)^(1/4)
Result: (9z^5)^(1/4) / z^5
Simplify: z(9z)^(1/4) / z^5
Again: (9z)^(1/4) / z^4

I believe I worked this correctly, but I have doubts when I read the answer sheet in the book with the solution: (9z^3)^(1/4) / z^2
Did I miss a step?
Thanks in advance... George
Found 3 solutions by Fombitz, CharlesG2, solver91311:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Here's the misstep.
Then I multiplied top and bottom by (z^5)^(1/4)
Let me simplify
A%5E%281%2F4%29%2AA%5E%281%2F4%29=A%5E%281%2F4%2B1%2F4%29=A%5E%281%2F2%29 and not A as you have it.
In your case, A=z%5E5
.
.
.
%289%2Fz%5E5%29%5E%281%2F4%29=%289z%5E%28-5%29%29%5E%281%2F4%29
%289%2Fz%5E5%29%5E%281%2F4%29=9%5E%281%2F4%29%2Az%5E%28-5%2F4%29

Answer by CharlesG2(834) About Me  (Show Source):
You can put this solution on YOUR website!
"Good morning!
An interesting radical conundrum for me:
SIMPLIFY: fourth root of (9 / z^5) or (9 / z^5)^(1/4)
I broke it down: (9)^(1/4) / (z^5)^(1/4)
Then I multiplied top and bottom by (z^5)^(1/4)
Result: (9z^5)^(1/4) / z^5
Simplify: z(9z)^(1/4) / z^5
Again: (9z)^(1/4) / z^4
I believe I worked this correctly, but I have doubts when I read the answer sheet in the book with the solution: (9z^3)^(1/4) / z^2
Did I miss a step?
Thanks in advance... George"
...
lets see
sorry for accidentally hitting post
(9 / z^5)^(1/4)
equals
9^(1/4) * (z^(-5))^(1/4)
equals
9^(1/4) * z^(-5/4)
multiply top and bottom by z^(3/4)
to get
9^(1/4) * z^(3/4) * z^(-2) (5/4 + 3/4 = 8/4 = 2)
or
9^(1/4) * (z^3)^(1/4) * (z^(-8))^(1/4)
(3^(1/2))^4 = 3^(4/2) = 3^2 = 9
(z^(3/4))^4 = z^(3/4 * 4) = z^3
(z^(-8/4)^4 = (z^(-2))^4 = z^(-8)
to get
3^(1/2) * z^(3/4) * z^(-2) (this equivalent to your book answer)
or
3^(1/2) * z^(-5/4)
or
+3%5E%281%2F2%29%2Fz%5E%285%2F4%29+
you said book had solution: (9z^3)^(1/4) / z^2
which is equivelent to 3^(1/2) * z^(3/4) * z^(-2)





Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


I see one problem right off.

You said that you began with:



True enough. So far, so good. But then you did this:




What you needed to do was:



Hint:



John