(5/4) to the power of 2 in fraction form

(5/4) to the power of 2 in fraction form

The Correct Answer and Explanation is:

The expression (\left(\frac{5}{4}\right)^2) means raising the fraction (\frac{5}{4}) to the power of 2. This involves multiplying (\frac{5}{4}) by itself. Here’s how to solve it step by step:

Step 1: Write the expression

[
\left(\frac{5}{4}\right)^2 = \frac{5}{4} \times \frac{5}{4}
]

Step 2: Multiply the numerators

The numerator of the resulting fraction is obtained by multiplying the numerators of the two fractions:

[
5 \times 5 = 25
]

Step 3: Multiply the denominators

The denominator of the resulting fraction is obtained by multiplying the denominators of the two fractions:

[
4 \times 4 = 16
]

Step 4: Simplify the result

After multiplying the numerators and denominators, we get the following:

[
\frac{25}{16}
]

Final Answer

The result of (\left(\frac{5}{4}\right)^2) is:

[
\frac{25}{16}
]

Explanation

Exponentiation, in this case, involves raising a fraction to a power. When you raise a fraction to a power, you apply the exponent to both the numerator and the denominator separately. Specifically, (\left(\frac{a}{b}\right)^n) means that both (a) (the numerator) and (b) (the denominator) are raised to the power of (n).

For example, (\left(\frac{5}{4}\right)^2) can be thought of as multiplying the fraction (\frac{5}{4}) by itself. This results in multiplying the numerators (5 and 5) and the denominators (4 and 4) individually. This is a basic application of the laws of exponents for fractions.

The fraction (\frac{25}{16}) cannot be simplified further since 25 and 16 do not have any common factors besides 1. Therefore, the final result is (\frac{25}{16}), which is the simplest form of the answer.