Calculate the Square of 4/5: Fraction Power Problem

To solve the problem of finding the value of $\left(\frac{4}{5}\right)^2$, we will follow these steps:

• Step 1: Identify the numerator and the denominator of the fraction. Here, the numerator is 4, and the denominator is 5.
• Step 2: Apply the exponent to both the numerator and the denominator separately: $\left(\frac{4}{5}\right)^2 = \frac{4^2}{5^2}$.
• Step 3: Calculate $\frac{4^2}{5^2}$. This gives:
  • The square of the numerator is $4^2 = 16$.
  • The square of the denominator is $5^2 = 25$.
  Thus, $\frac{4^2}{5^2} = \frac{16}{25}$.

Since we successfully calculated $\left(\frac{4}{5}\right)^2 = \frac{16}{25}$, this matches the choice labeled $\frac{16}{25}$.

Therefore, the correct expression is $\frac{16}{25}$.