Question: Evaluate.
$\left(\frac{4}{5}\right)^2 - \frac{1}{4}$
1. **State the problem:** Evaluate the expression $$\left(\frac{4}{5}\right)^2 - \frac{1}{4}$$.
2. **Recall the formula:** Squaring a fraction means squaring both numerator and denominator: $$\left(\frac{a}{b}\right)^2 = \frac{a^2}{b^2}$$.
3. **Calculate the square:** $$\left(\frac{4}{5}\right)^2 = \frac{4^2}{5^2} = \frac{16}{25}$$.
4. **Rewrite the expression:** Now the expression is $$\frac{16}{25} - \frac{1}{4}$$.
5. **Find a common denominator:** The denominators are $25$ and $4$. The least common denominator (LCD) is $$25 \times 4 = 100$$.
6. **Convert fractions to have the LCD:**
$$\frac{16}{25} = \frac{16 \times 4}{25 \times 4} = \frac{64}{100}$$
$$\frac{1}{4} = \frac{1 \times 25}{4 \times 25} = \frac{25}{100}$$
7. **Subtract the fractions:**
$$\frac{64}{100} - \frac{25}{100} = \frac{64 - 25}{100} = \frac{39}{100}$$
8. **Final answer:** $$\boxed{\frac{39}{100}}$$ or $0.39$ in decimal form.