Find the Product of Powers Given a Linear Equation

If $5x + 3y = 3$, then find $32^x \times 8^y$.

In this problem, the student is tasked with finding the value of an expression involving powers given a linear equation in two variables. The core concept involves understanding how to manipulate and work with equations to find the values of variables that satisfy certain conditions.

A common strategy when solving problems of this type is to first isolate one variable in terms of the other using the given equation. Once this connection is made, you can substitute the known relationship back into the expression you need to evaluate. This particular problem also involves concepts from exponents since it requires evaluating an expression of the form $a^x \times b^y$.

Understanding how to handle expressions involving powers is critical here, especially the property that relates different bases when they can be written with a common base, such as recognizing that both 32 and 8 are powers of 2. This conceptual knowledge will allow the student to simplify the expressions and find the product efficiently. Therefore, this problem not only tests algebraic manipulation skills but also encourages exposure to strategies used in dealing with exponential expressions.