^3sqrt-375x^6y^4

Answer 1

To simplify ^3√(-375x^6y^4), we can rewrite it as (-375x^6y^4)^(1/3).

To simplify, we can break down the expression into its individual factors and simplify each factor separately.

-375 can be written as -3 * 5 * 5 * 5.
x^6 can be written as (x^2)^3.
y^4 can be written as (y^2)^2.

Substituting the simplified factors back into the expression, we get:

[(-3 * 5 * 5 * 5 * (x^2)^3 * (y^2)^2)^(1/3)]

Taking out -1 from the cube root of -375:

-1 * [(3 * 5 * 5 * 5 * (x^2)^3 * (y^2)^2)^(1/3)]

Breaking down the factors inside the cube root:

-1 * [(3^(1/3) * (5^3)^(1/3) * ((x^2)^3)^(1/3) * ((y^2)^2)^(1/3)]

Simplifying each factor:

-1 * [(3^(1/3) * 5 * x^2 * y^(2/3))]

So, the simplified form of ^3√(-375x^6y^4) is -1 * (3^(1/3) * 5 * x^2 * y^(2/3)).