# Divide fifth root of x^1625 root of x^20

x165x2025
Rewrite x16 as (x3)5x.
Factor out x15.
x15x5x2025
Rewrite x15 as (x3)5.
(x3)5x5x2025
(x3)5x5x2025
Pull terms out from under the radical.
x3x5x2025
Rewrite x20 as (x4)5.
x3x5(x4)525
Rewrite (x4)525 as (x4)555.
x3x5(x4)555
Pull terms out from under the radical, assuming real numbers.
x3x5x45
Multiply x3x5x45.
Combine using the product rule for radicals.
x3x4x5
Multiply x4 by x by adding the exponents.
Multiply x4 by x.
Raise x to the power of 1.
x3x4x15
Use the power rule aman=am+n to combine exponents.
x3x4+15
x3x4+15
x3x55
x3x55
x3x55
Pull terms out from under the radical, assuming real numbers.
x3x
Multiply x3 by x by adding the exponents.
Multiply x3 by x.
Raise x to the power of 1.
x3x1
Use the power rule aman=am+n to combine exponents.
x3+1
x3+1