Answer
$x^{\frac{7 }{12}}$
Work Step by Step
Use the rule $a^m \cdot a^n = a^{m+n}$:
$x^{\frac{3}{4}}x^{\frac{1}{3}}x^{-\frac{1}{2}}=x^{\frac{3}{4}+\frac{1}{3}-\frac{1}{2}}$
The LCD of the exponents is $12$.
Make the fractions similar using their LCD to obtain:
$=x^{\frac{3\cdot3 }{4\cdot3}+\frac{1\cdot 4}{3\cdot 4}-\frac{1\cdot 6}{2\cdot 6}}$
$=x^{\frac{9 }{12}+\frac{ 4}{12}-\frac{ 6}{12}}$
Simplify to obtain:
$=x^{\frac{9+4-6 }{12}}$
$=x^{\frac{7 }{12}}$
Hence, the correct answer is $x^{\frac{7 }{12}}$.
