To simplify the expression [tex]\(\frac{a^4 b^4}{a^4 b^4}\)[/tex], follow these steps:
1. Understand the Expression: The denominator and the numerator are identical, i.e., both are [tex]\(a^4 b^4\)[/tex].
2. Apply Basic Division Property: Any non-zero number divided by itself is equal to 1. This property holds true for expressions involving variables and exponents as well.
3. Simplify: Divide the numerator by the denominator:
[tex]\[
\frac{a^4 b^4}{a^4 b^4} = 1
\][/tex]
Therefore, the correct simplification of the expression [tex]\(\frac{a^4 b^4}{a^4 b^4}\)[/tex] is 1.
None of the other options given (like [tex]\(a^9 b^{10}\)[/tex], [tex]\(a b^2\)[/tex], [tex]\(\frac{1}{a b^2}\)[/tex], and [tex]\(\frac{1}{a^9 b^{10}}\)[/tex]) match this simplified result.
Hence, the correct simplification is:
[tex]\[ 1 \][/tex]
