We are asked to simplify the expression $(2x^{\frac{1}{4}}y^{\frac{1}{6}})(-5x^{\frac{1}{6}}y^{\frac{-1}{8}})$ and express the answer with positive exponents.

1. Problem Description

We are asked to simplify the expression $(2x^{\frac{1}{4}}y^{\frac{1}{6}})(-5x^{\frac{1}{6}}y^{\frac{-1}{8}})$ and express the answer with positive exponents.

2. Solution Steps

First, multiply the coefficients and variables with the same base.

$(2x^{\frac{1}{4}}y^{\frac{1}{6}})(-5x^{\frac{1}{6}}y^{\frac{-1}{8}}) = (2)(-5)x^{\frac{1}{4}}x^{\frac{1}{6}}y^{\frac{1}{6}}y^{\frac{-1}{8}}$

$= -10x^{\frac{1}{4}+\frac{1}{6}}y^{\frac{1}{6}-\frac{1}{8}}$

Now, we need to find a common denominator for the exponents.

$\frac{1}{4} + \frac{1}{6} = \frac{3}{12} + \frac{2}{12} = \frac{5}{12}$

$\frac{1}{6} - \frac{1}{8} = \frac{4}{24} - \frac{3}{24} = \frac{1}{24}$

So the expression becomes:

$-10x^{\frac{5}{12}}y^{\frac{1}{24}}$

3. Final Answer

$-10x^{\frac{5}{12}}y^{\frac{1}{24}}$