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.Com
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) (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
and not as you have it.
In your case,
.
.
.
Answer by CharlesG2(834) (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
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) (Show Source): You can put this solution on YOUR website!
I see one problem right off.
You said that you began with:
^{\frac{1}{4}}\ =\ \frac{9^{\frac{1}{4}}}{\left(z^5\right)^{\frac{1}{4}}})
True enough. So far, so good. But then you did this:
^{\frac{1}{4}}}\right)\left(\frac{\left(z^5\right)^{\frac{1}{4}}}{\left(z^5\right)^{\frac{1}{4}}}\right)\ =\ \frac{\left(9z^5\right)^{\frac{1}{4}}}{\left(z^5\right)^{\frac{2}{4}}}\ \neq\ \frac{\left(9z^5\right)^{\frac{1}{4}}}{z^5})
What you needed to do was:
^{\frac{1}{4}}}\right)\left(\frac{\left(z^5\right)^{\frac{3}{4}}}{\left(z^5\right)^{\frac{3}{4}}}\right)\ = \frac{z^3\left(9z^3\right)^{\frac{1}{4}}}{z^5}\ =\ \frac{\left(9z^3\right)^{\frac{1}{4}}}{z^2})
Hint:
^{\frac{3}{4}}\ =\ z^{\frac{15}{4}}\ =\ z^3\cdot z^{\frac{3}{4}}\ =\ z^3\cdot (z^3)^{\frac{1}{4}})
John
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