Simplify fourth root of (5x)/(8y)

Math
5x8y4
Rewrite 5x8y4 as 5x48y4.
5x48y4
Multiply 5x48y4 by 8y438y43.
5x48y4⋅8y438y43
Combine and simplify the denominator.
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Multiply 5x48y4 and 8y438y43.
5x48y438y48y43
Raise 8y4 to the power of 1.
5x48y438y418y43
Use the power rule aman=am+n to combine exponents.
5x48y438y41+3
Add 1 and 3.
5x48y438y44
Rewrite 8y44 as 8y.
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Use axn=axn to rewrite 8y4 as (8y)14.
5x48y43((8y)14)4
Apply the power rule and multiply exponents, (am)n=amn.
5x48y43(8y)14⋅4
Combine 14 and 4.
5x48y43(8y)44
Cancel the common factor of 4.
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Cancel the common factor.
5x48y43(8y)44
Divide 1 by 1.
5x48y43(8y)1
5x48y43(8y)1
Simplify.
5x48y438y
5x48y438y
5x48y438y
Simplify the numerator.
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Rewrite 8y43 as ((8y)3)14.
5×4(8y)348y
Apply the product rule to 8y.
5x483y348y
Raise 8 to the power of 3.
5x4512y348y
Rewrite 512y3 as 44⋅(2y3).
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Factor 256 out of 512.
5×4256(2)y348y
Rewrite 256 as 44.
5×444⋅2y348y
Add parentheses.
5×444⋅(2y3)48y
5×444⋅(2y3)48y
Pull terms out from under the radical.
5×4⋅42y348y
Combine exponents.
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Combine using the product rule for radicals.
45x(2y3)48y
Multiply 2 by 5.
410xy348y
410xy348y
410xy348y
Cancel the common factor of 4 and 8.
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Factor 4 out of 410xy34.
4(10xy34)8y
Cancel the common factors.
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Factor 4 out of 8y.
4(10xy34)4(2y)
Cancel the common factor.
410xy344(2y)
Rewrite the expression.
10xy342y
10xy342y
10xy342y
Simplify fourth root of (5x)/(8y)

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