standard_description: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define 5^(1/3) to be the cube root of 5 because we want (5^(1/3))^(3) = 5(^(1/3))^(3) to hold, so (5^(1/3))^(3) must equal 5.
problem_activity: A red-throated loon is a type of diving bird that dives for its food. One particular loon dives for 8 seconds to a depth of 12 feet under the surface of the water.
a.   Assume the loon dives at a constant rate. Write an equation that can be used to represent the elevation,
$$y$$
, of the loon after
$$x$$
seconds into the dive.
b.   If the loon is at a depth of 22.5 feet under the surface of the water, how long was it diving for?


aligns: no