Using the properties of exponents, which expression is equivalent to x1/6⋅x1/6?(1 point)

Question

Responses

x−−√3/6
root index 3/6 Start Root x End Root

x−−√
Start Root x End Root

1x√3
Start Fraction 1 over root index 3 Start Root x End Root End Fraction

x−−√3
root index 3 Start Root x End Root

Answer 1

To simplify the expression \( x^{1/6} \cdot x^{1/6} \), we can use the properties of exponents.

1. When multiplying with the same base, we add the exponents: \[ x^{1/6} \cdot x^{1/6} = x^{1/6 + 1/6} = x^{2/6} = x^{1/3} \]

2. Now, we can rewrite \( x^{1/3} \) in radical form: \[ x^{1/3} = \sqrt[3]{x} \]

Looking at your options:

• \( \sqrt[3]{x} \) is equivalent to \( x^{1/3} \).

Thus, the correct response is:

root index 3 Start Root x End Root.