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).