Use the grouping symbols to interpret the following equation: x/8=3^(x+4)/2 . Which expression in the equation represents a product?

1 answer

Let's analyze the equation given:

\[ \frac{x}{8} = \frac{3^{(x+4)}}{2} \]

To identify which part of this equation represents a product, let's break down the expressions on both sides of the equation.

On the left side, we have:

\[ \frac{x}{8} \]

This can also be interpreted as \(x \cdot \frac{1}{8}\), which does indeed contain a product (between \(x\) and \(\frac{1}{8}\)).

On the right side, we see:

\[ \frac{3^{(x+4)}}{2} \]

This can be expressed as \(3^{(x+4)} \cdot \frac{1}{2}\). The expression \(3^{(x+4)}\) itself does not represent a product, but when multiplied by \(\frac{1}{2}\), the overall, this side of the equation includes a product as well.

However, the term that stands out as clearly representing a product on either side is:

  1. On the left: \(x \cdot \frac{1}{8}\)
  2. On the right: \(3^{(x+4)} \cdot \frac{1}{2}\)

So, the expression that represents a product in this equation can be:

  • \(x \cdot \frac{1}{8}\) from the left side, or
  • \(3^{(x+4)} \cdot \frac{1}{2}\) from the right side.

In conclusion, both sides contain expressions where products are present, specifically:

  • \( \frac{x}{8} \) as \(x \cdot \frac{1}{8}\)
  • \( \frac{3^{(x+4)}}{2} \) as \(3^{(x+4)} \cdot \frac{1}{2}\)