Question

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

1/x√3
the fraction with numerator 1 and denominator cube root of x

x−−√
square root of x

x−−√3
cube root of x

x−−√36

Answer 1

To simplify the expression \( x^{1/6} \cdot x^{1/6} \), we 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, let’s rewrite \( x^{1/3} \) in a different way:

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

So, the correct equivalent expression is:

**cube root of x**.

If you were asked to select from the mentioned options, "cube root of x" \( \sqrt[3]{x} \) is the correct response.