Complete the Expression: Finding the Equal Value of 3^(x-y)

Insert the corresponding expression:

$3^{x-y}=$

To solve the problem, we need to understand the Power of a Quotient Rule for Exponents. The rule states that:

• If you have a power of the quotient, such as: $(\frac{a}{b})^n$, it can also be expressed as: $\frac{a^n}{b^n}$

In the given expression, we have $3^{x-y}$. This can be rewritten using the inverse of the rule as:

$3^{x-y} = \frac{3^x}{3^y}$

Here’s a step-by-step breakdown:

1. Start with the expression: $3^{x-y}$.
2. Using the law of exponents, which states that $a^{m-n} = \frac{a^m}{a^n}$, we rewrite the expression.
3. Replace $a$ with $3$, $m$ with $x$, and $n$ with $y$ to get: $3^{x-y} = \frac{3^x}{3^y}$.

The solution to the question is: $\frac{3^x}{3^y}$