Using the properties of exponents, which expression is equivalent to x 1/6 ⋅ x 1/6

To simplify the expression x^(1/6) ⋅ x^(1/6), you can use the property of exponents that states x^m ⋅ x^n = x^(m + n) when the base is the same.

In this case, the base is x, and the exponents are both 1/6. Applying the exponent property, we can add the exponents together:

x^(1/6) ⋅ x^(1/6) = x^((1/6) + (1/6))

Simplifying the exponent, we get:

x^(1/6 + 1/6) = x^(2/6)

Since 2/6 simplifies to 1/3, we can rewrite the expression as:

x^(2/6) = x^(1/3)

Therefore, the expression x^(1/6) ⋅ x^(1/6) is equivalent to x^(1/3).

By using the properties of exponents, we can simplify the expression x^(1/6) ⋅ x^(1/6) by adding the exponents:

x^(1/6) ⋅ x^(1/6) = x^(1/6 + 1/6) = x^(2/6)
Since 2/6 simplifies to 1/3, the expression is equivalent to x^(1/3).