few_shots: 
Example:
Concept/skill: 
Recognize and represent proportional relationships between quantities.

Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Answer: 
No. Usually problems that teach recognizing and representing proportional relationships between quantities involve deciding whether two quantities are in a proportional relationship or identifying the constant of proportionality, and then representing proportional relationships by equations or explaining proportional relationship using coordinate graphs.

Now, determine whether the following problem or activity can enable students to understand the concepts or skills in the provided description.

shot_info: fl_problem_000972_neg_0

6
standard_description: Use the relation i^(2) = –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
problem_activity: Provide a written explanation for each question below.
a.   Is it true that
$${\left(1000^{1\over3}\right)^3=(1000^3)^{1\over3}}$$
? Explain or show how you know.
b.   Is it true that
$${\left(4^{1\over2}\right)^3=(4^3)^{1\over2}}$$
? Explain or show how you know.
c.   Suppose that
$$m$$
and
$$n$$
are positive integers and
$$b$$
is a real number so that the principal
$$n^{th}$$
root of
$$b$$
exists. In general, does
$$\left(b^{1\over n}\right)^m=(b^m)^{1\over n}$$
? Explain or show how you know.


aligns: no