To simplify the expression \(\frac{(x + 2y)^7}{(x + 2y)^2}\), follow these steps:
1. Identify the Common Base: Notice that both the numerator and the denominator have the same base \((x + 2y)\).
2. Apply the Laws of Exponents: When dividing expressions with the same base, subtract the exponent of the denominator from the exponent of the numerator. This can be written as:
[tex]\[
\frac{(x + 2y)^7}{(x + 2y)^2} = (x + 2y)^{7-2}
\][/tex]
3. Subtract the Exponents: Calculate the exponent in the subtracted form:
[tex]\[
7 - 2 = 5
\][/tex]
4. Simplify the Expression: Substitute the simplified exponent back into the expression:
[tex]\[
(x + 2y)^5
\][/tex]
So, the simplified form of the expression \(\frac{(x + 2y)^7}{(x + 2y)^2}\) is:
[tex]\[
(x + 2y)^5
\][/tex]
