Answer
$14x^{\frac{7}{12}}$
Work Step by Step
$$(7x^{\frac{1}{3}})(2x^{\frac{1}{4}})$$ $$=(7\times2)(x^{\frac{1}{3}}\times x^{\frac{1}{4}})$$
When two rational expressions with the same base are multiplied, add the exponents.
$$=14x^{\frac{1}{3} + \frac{1}{4}}$$
When adding fractions, you need a common denominator, in this case, 12:
$$=14x^{\frac{4}{12}+\frac{3}{12}}$$ $$=14x^\frac{7}{12}$$
