Simplify by factoring Assume mat all variables in the radica

Simplify by factoring Assume mat all variables in the radicand represent positive real numbers and that the radicand does not involve negative quantities raised to even powers. 3 Squareroot 3125x^17 y^9 3 Squareroot 3125x^17 y^9 = (Simplify your answer. Type an exact answer. using radicals as needed)

Solution

³(3125x¹⁷y⁹)

=(3125x¹⁷y⁹)^1_/3

=(3125)^1_/3(x¹⁷)^1_/3(y⁹)^1_/3

=(5⁵)^1_/3x^17_/3y^9_/3

=5^5_/3x^17_/3y^9_/3

=5^5_/3 x^17_/3 y³

= y³ (5*5^2_/3)(x⁵*x^2_/3)

= 5x⁵y³ (5^2_/3x^2_/3)

= 5x⁵y³ (5²x²)^1_/3

= 5x⁵y³ (25x²)^1_/3

= 5x⁵y³ (³(25x²))