(5/4)^2 in a fraction in simplest form
The Correct Answer and Explanation is :
To simplify ((\frac{5}{4})^2) and express it as a fraction in simplest form, follow these steps:
- Square the Numerator and Denominator: When you square a fraction, you square both the numerator and the denominator. Thus, we have: [
\left(\frac{5}{4}\right)^2 = \frac{5^2}{4^2}
] This means: [
= \frac{25}{16}
] - Check for Simplification: Next, we check if the fraction (\frac{25}{16}) can be simplified. A fraction is simplified when the numerator and the denominator have no common factors other than 1. The numerator, 25, can be factored as (5 \times 5) (or (5^2)), and the denominator, 16, can be factored as (4 \times 4) (or (2^4)). The only common factor between 25 and 16 is 1. Since they do not share any other factors, (\frac{25}{16}) is already in its simplest form.
- Final Answer: Therefore, the simplified form of ((\frac{5}{4})^2) is: [
\frac{25}{16}
]
Explanation
When working with fractions, squaring the fraction involves squaring both the top (numerator) and the bottom (denominator). This follows the rule that states ((\frac{a}{b})^n = \frac{a^n}{b^n}). It’s essential to always check if the resulting fraction can be simplified, as understanding how to reduce fractions is a fundamental skill in mathematics.
In this case, both 25 and 16 are powers of prime numbers (5 and 2, respectively), and since they share no common prime factors, the fraction remains unchanged. Recognizing that the fraction is in its simplest form helps maintain clarity and precision in mathematical communication, ensuring that the results are accurate and understandable.
Thus, the expression ((\frac{5}{4})^2) simplifies to (\frac{25}{16}), which is its simplest fractional form.