A logistics analyst is using a formula to estimate the growth of shipping costs, which results in the expression ${}27^{\frac{2}{3}}$. To simplify this value, the analyst must rewrite it in its radical form. Which of the following is the correct radical representation of ${}27^{\frac{2}{3}}$?

An interior designer is calculating the area of a customized hexagonal tile pattern using the expression ${}27^{\frac{2}{3}}$. Match each step or result of the simplification process with its correct mathematical form or numerical value.

A construction foreman is estimating the volume of a concrete foundation using the mathematical expression ${}4^{\frac{3}{2}}$. True or False: To simplify this expression according to the standard order of operations for rational exponents, the foreman should first find the square root of 4 and then cube that result.

An urban planner is using a scaling factor of ${}27^{\frac{2}{3}}$ to determine the area of a new community park. Arrange the following steps in the correct order to simplify this expression using the radical form $a^{\frac{m}{n}} = (\sqrt[n]{a})^m$.

An architectural drafter is calculating the dimensions of a scaled model using a scaling factor of ${}4^{\frac{3}{2}}$. To evaluate this expression by hand and keep the intermediate numbers small, the drafter converts it to radical form. The denominator of the exponent (2) dictates taking the square root of 4. The numerator of the exponent (3) dictates raising that result to the power of ____.