Answer
$x^{\frac{11}{12}}$
Work Step by Step
Use the rule $a^m \cdot a^n = a^{m+n}$, then simplify to obtain:
$x^{\frac{2}{3}}x^{\frac{1}{2}}x^{-\frac{1}{4}}=x^{\frac{2}{3}+\frac{1}{2}-\frac{1}{4}}$
The LCD of the exponents is $12$.
Make the fractions similar using their LCD:
$=x^{\frac{2\cdot4 }{3\cdot4}+\frac{1\cdot 6}{2\cdot 6}-\frac{1\cdot 3}{4\cdot 3}}$
$=x^{\frac{8 }{12}+\frac{ 6}{12}-\frac{ 3}{12}}$
Simplify to obtain:
$=x^{\frac{8+6-3 }{12}}$
$=x^{\frac{11}{12}}$
Hence, the correct answer is $x^{\frac{11}{12}}$.
