Answer
$x^{1/2}$
Work Step by Step
When we multiply two exponents that have the same base, we keep the base as-is and add the exponents:
$x^{1/6}\cdot x^{1/3}$ = $x^{1/6 + 1/3}$
Because the fractions have different denominators, we have to find equivalent fractions that have the same denominator. The least common denominator for these two fractions is $6$. Let's rewrite the problem using equivalent fractions with the same denominators:
$x^{1/6 + 2/6}$
We can add the fractional exponents now:
$x^{3/6}$
Divide the fraction by the greatest common factor of both the numerator and denominator, which is $3$:
$x^{1/2}$
