x165x2025

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

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

Add 4 and 1.

x3x55

x3x55

x3x55

Pull terms out from under the radical, assuming real numbers.

x3x

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

Add 3 and 1.

x4

x4

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