Simplify fourth root of (5x)/(243y^16)

Math
5x243y164
Rewrite 5x243y16 as (13y4)45×3.
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Factor the perfect power 14 out of 5x.
14(5x)243y164
Factor the perfect power (3y4)4 out of 243y16.
14(5x)(3y4)4⋅34
Rearrange the fraction 14(5x)(3y4)4⋅3.
(13y4)45×34
(13y4)45×34
Pull terms out from under the radical.
13y45x34
Rewrite 5×34 as 5×434.
13y4⋅5×434
Multiply 5×434 by 343343.
13y4(5×434⋅343343)
Combine and simplify the denominator.
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Multiply 5×434 and 343343.
13y4⋅5×434334343
Raise 34 to the power of 1.
13y4⋅5×4343341343
Use the power rule aman=am+n to combine exponents.
13y4⋅5×4343341+3
Add 1 and 3.
13y4⋅5×4343344
Rewrite 344 as 3.
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Use axn=axn to rewrite 34 as 314.
13y4⋅5×4343(314)4
Apply the power rule and multiply exponents, (am)n=amn.
13y4⋅5×4343314⋅4
Combine 14 and 4.
13y4⋅5×4343344
Cancel the common factor of 4.
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Cancel the common factor.
13y4⋅5×4343344
Divide 1 by 1.
13y4⋅5×434331
13y4⋅5×434331
Evaluate the exponent.
13y4⋅5×43433
13y4⋅5×43433
13y4⋅5×43433
Simplify the numerator.
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Rewrite 343 as (33)14.
13y4⋅5×43343
Raise 3 to the power of 3.
13y4⋅5×42743
13y4⋅5×42743
Simplify the numerator.
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Combine using the product rule for radicals.
13y4⋅5x⋅2743
Multiply 27 by 5.
13y4⋅135×43
13y4⋅135×43
Multiply 13y4⋅135×43.
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Multiply 13y4 and 135×43.
135x43y4⋅3
Multiply 3 by 3.
135x49y4
135x49y4
Simplify fourth root of (5x)/(243y^16)

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