Simplify the Expression: 20^(x+y) ÷ 20^(a+y) Using Exponent Rules

Let's start by analyzing the given expression $\frac{20^{x+y}}{20^{a+y}}$.

We have a fraction with the same base number in both the numerator and the denominator.

According to the Power of a Quotient Rule for Exponents, for any non-zero number $b$ and integers $m$ and $n$, $\frac{b^m}{b^n} = b^{m-n}$.

This means we can subtract the exponents of the denominator from the exponents of the numerator. First, write down the exponents explicitly:

• Numerator: $x + y$
• Denominator: $a + y$

Next, apply the rule:

$\frac{20^{x+y}}{20^{a+y}} = 20^{(x+y)-(a+y)}$

Distribute the subtraction in the exponent:

$20^{x+y-a-y}$

Simplify the terms:

As the variable $y$ is present in both terms, they cancel each other out, resulting in:

$20^{x-a}$

This is the simplest form for the expression, and it matches the provided correct answer.

The solution to the question is: $20^{x-a}$