5x8y4

Rewrite 5x8y4 as 5x48y4.

5x48y4

Multiply 5x48y4 by 8y438y43.

5x48y4⋅8y438y43

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.

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.

Cancel the common factor.

5x48y43(8y)44

Divide 1 by 1.

5x48y43(8y)1

5x48y43(8y)1

Simplify.

5x48y438y

5x48y438y

5x48y438y

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).

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.

Combine using the product rule for radicals.

45x(2y3)48y

Multiply 2 by 5.

410xy348y

410xy348y

410xy348y

Factor 4 out of 410xy34.

4(10xy34)8y

Cancel the common factors.

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)