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

Question

Responses

x−−√
Start Root x End Root

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

x−−√36
root index 36 Start Root x End Root

1x√3

Answer 1

To simplify the expression \( x^{1/6} \cdot x^{1/6} \), you can use the property of exponents that states \( a^m \cdot a^n = a^{m+n} \).

In this case:

\[ x^{1/6} \cdot x^{1/6} = x^{(1/6) + (1/6)} = x^{2/6} = x^{1/3} \]

Now, \( x^{1/3} \) can also be written in radical form as:

\[ x^{1/3} = \sqrt[3]{x} \]

This corresponds to the response:

\[ \text{root index 3 } \sqrt{x} \]

So the correct answer is:

\(\text{root index 3 Start Root x End Root}\)