SOLUTION: 1) 3√30x^15/120x^17y^-1 It is a cube root. 2)3√4√10=100^2x There's 10 inside of cube root and 4th root. 3)9√(2xy^4)^-12/(8x^12y)^2 It is a

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 1) 3√30x^15/120x^17y^-1 It is a cube root. 2)3√4√10=100^2x There's 10 inside of cube root and 4th root. 3)9√(2xy^4)^-12/(8x^12y)^2 It is a       Log On


   

Question 393681: 1)
3√30x^15/120x^17y^-1
It is a cube root.
2)3√4√10=100^2x
There's 10 inside of cube root and 4th root.
3)9√(2xy^4)^-12/(8x^12y)^2
It is a 9th root.


Thank you so much!!!!!! I have a test on Friday and my teacher really can't teach :(
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
1)3√30x^15/120x^17y^-1
It is a cube root.
---
[cbrt(30x^15)]/[120x^17y^-1)]
----
[x^5*y*cbrt(30)]/[120x^17]
----
[y*cbrt(30)]/[24x^12]
==========================

2)3√4√10=100^2x
There's 10 inside of cube root and 4th root.
---
10^(1/12) = [10^2]^(2x)
---
10^(1/12) = 10^(4x)
---
4x = 1/12
x = 1/48
==================
3)9√(2xy^4)^-12/(8x^12y)^2
It is a 9th root.
---
(2xy^4)^(-12/9) / (64x^24y^2)
---
(2xy^4)^(-4/3) / (2^6*x^24y^2)
[2^(-4/3)*x^(-4/3)*y^(-16/3)]/[2^6*x^24*y^2]
---
= 1/[2^(22/3)*x^23*y^(22/3)
===
There are a number of forms the next step could take.
I'll leave it to you. Sometimes the answer book will
show one form and you have an equivalent other form.
Try to determine whether the two forms are equivalent.
If they are you have found the solution.
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Cheers,
Stan H.