Question 393681
1)3√30x^15/120x^17y^-1 
It is a cube root.
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[cbrt(30x^15)]/[120x^17y^-1)]
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[x^5*y*cbrt(30)]/[120x^17]
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[y*cbrt(30)]/[24x^12]
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2)3√4√10=100^2x 
There's 10 inside of cube root and 4th root.
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10^(1/12) = [10^2]^(2x)
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10^(1/12) = 10^(4x)
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4x = 1/12
x = 1/48
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3)9√(2xy^4)^-12/(8x^12y)^2 
It is a 9th root.
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(2xy^4)^(-12/9) / (64x^24y^2)
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(2xy^4)^(-4/3) / (2^6*x^24y^2)
[2^(-4/3)*x^(-4/3)*y^(-16/3)]/[2^6*x^24*y^2]
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= 1/[2^(22/3)*x^23*y^(22/3)
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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.