Question

What is the simplified form of the sixth root of x times the sixth root of x times the sixth root of x times the sixth root of x?

Answer 1

The simplified form of the sixth root of x multiplied by itself four times is x to the power of two-thirds (x^(2/3)).

Step-by-step explanation:

The simplified form of the sixth root of x times the sixth root of x times the sixth root of x times the sixth root of x is found by considering the properties of exponents. Multiplying roots with the same index (the sixth root, in this case) corresponds to multiplying the exponents of the radicands when written as fractional exponents. Since the sixth root of x can be written as x^(1/6), the product of four such roots would be x^(1/6) × x^(1/6) × x^(1/6) × x^(1/6), which simplifies to x^(4/6) by adding the exponents. Alternatively, this simplifies further to x^(2/3).

Answer 2

x^(1/6) · x^(1/6) · x^(1/6) ·x^(1/6) = x^(4/6) since we add the exponents

4/6 can be simplified to 2/3

The simplified form is x^(2/3)