Simplify – square root of (27x^3)/(y^5)

Math
-27x3y5
Rewrite 27x3y5 as (3xy2)23xy.
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Factor the perfect power (3x)2 out of 27×3.
-(3x)2⋅(3x)y5
Factor the perfect power (y2)2 out of y5.
-(3x)2⋅(3x)(y2)2y
Rearrange the fraction (3x)2⋅(3x)(y2)2y.
-(3xy2)23xy
-(3xy2)23xy
Pull terms out from under the radical.
-(3xy23xy)
Rewrite 3xy as 3xy.
-(3xy2⋅3xy)
Multiply 3xy by yy.
-(3xy2(3xy⋅yy))
Combine and simplify the denominator.
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Multiply 3xy and yy.
-(3xy2⋅3xyyy)
Raise y to the power of 1.
-(3xy2⋅3xyy1y)
Raise y to the power of 1.
-(3xy2⋅3xyy1y1)
Use the power rule aman=am+n to combine exponents.
-(3xy2⋅3xyy1+1)
Add 1 and 1.
-(3xy2⋅3xyy2)
Rewrite y2 as y.
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Use axn=axn to rewrite y as y12.
-(3xy2⋅3xy(y12)2)
Apply the power rule and multiply exponents, (am)n=amn.
-(3xy2⋅3xyy12⋅2)
Combine 12 and 2.
-(3xy2⋅3xyy22)
Cancel the common factor of 2.
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Cancel the common factor.
-(3xy2⋅3xyy22)
Divide 1 by 1.
-(3xy2⋅3xyy1)
-(3xy2⋅3xyy1)
Simplify.
-(3xy2⋅3xyy)
-(3xy2⋅3xyy)
-(3xy2⋅3xyy)
Combine using the product rule for radicals.
-(3xy2⋅3xyy)
Multiply 3xy2⋅3xyy.
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Multiply 3xy2 and 3xyy.
-3x3xyy2y
Multiply y2 by y by adding the exponents.
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Multiply y2 by y.
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Raise y to the power of 1.
-3x3xyy2y1
Use the power rule aman=am+n to combine exponents.
-3x3xyy2+1
-3x3xyy2+1
Add 2 and 1.
-3x3xyy3
-3x3xyy3
-3x3xyy3
Simplify – square root of (27x^3)/(y^5)

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