To express the fraction [tex]\(\frac{121}{256}\)[/tex] as your final answer, follow these steps:
1. Identify the Numerator and Denominator:
The numerator of this fraction is [tex]\(121\)[/tex], and the denominator is [tex]\(256\)[/tex].
2. Verify if the Fraction is in Simplest Form:
To ensure the fraction [tex]\(\frac{121}{256}\)[/tex] is in its simplest form, we need to check if there are any common factors between the numerator and the denominator other than [tex]\(1\)[/tex].
- The number [tex]\(121\)[/tex] has the prime factorization of [tex]\(11 \times 11\)[/tex], which is [tex]\(11^2\)[/tex].
- The number [tex]\(256\)[/tex] is a power of [tex]\(2\)[/tex], specifically [tex]\(2^8\)[/tex].
Since [tex]\(11\)[/tex] (a prime number making up the numerator's prime factors) is not a factor of [tex]\(256\)[/tex], the numerator and denominator do not share any common factors other than [tex]\(1\)[/tex].
3. Conclusion:
Since there are no common factors other than [tex]\(1\)[/tex], the fraction [tex]\(\frac{121}{256}\)[/tex] is already in its simplest form.
Therefore, the fraction [tex]\(\frac{121}{256}\)[/tex] represents the final simplified answer.
