A data analyst is simplifying a performance optimization formula that involves rational exponents. Match each exponent property with the correct action used to simplify the expressions $\frac{u^{\frac{4}{5}} \cdot u^{-\frac{2}{5}}}{u^{-\frac{13}{5}}}$ and $\left(\frac{27 x^{\frac{4}{5}} y^{\frac{1}{6}}}{x^{\frac{1}{5}} y^{-\frac{5}{6}}}\right)^{\frac{1}{3}}$.

A laboratory technician is simplifying a sensor calibration formula: $\left(\frac{27 x^{\frac{4}{5}} y^{\frac{1}{6}}}{x^{\frac{1}{5}} y^{-\frac{5}{6}}}\right)^{\frac{1}{3}}$. According to the standard procedure for exponent properties, what is the correct first step to simplify the terms inside the parentheses?

A logistics manager is simplifying a volume-scaling formula for shipping containers: $\frac{u^{\frac{4}{5}} \cdot u^{-\frac{2}{5}}}{u^{-\frac{13}{5}}}$. To ensure the formula is correctly entered into the company's automated tracking system, the manager must simplify it to its most basic form. Arrange the following steps in the correct order to simplify this expression using exponent properties.

An inventory specialist is simplifying a resource allocation formula represented by the expression $\frac{u^{\frac{4}{5}} \cdot u^{-\frac{2}{5}}}{u^{-\frac{13}{5}}}$. According to the Product Property of exponents, the first step in simplifying the numerator results in $u^{\frac{2}{5}}$.

A quality control technician is using the expression $\left(\frac{27 x^{\frac{4}{5}} y^{\frac{1}{6}}}{x^{\frac{1}{5}} y^{-\frac{5}{6}}}\right)^{\frac{1}{3}}$ to model manufacturing tolerances. To simplify the terms inside the parentheses, they must recall the Quotient Property. For the $x$ variable, this property requires them to ____ the denominator's exponent from the numerator's exponent.