1. **State the problem:** Simplify the expression $$\left(\frac{4}{5}\right)^2 - \frac{1}{4}$$. 2. **Apply the exponent:** Square the fraction $$\frac{4}{5}$$ using the rule $$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$$. $$\left(\frac{4}{5}\right)^2 = \frac{4^2}{5^2} = \frac{16}{25}$$ 3. **Rewrite the expression:** $$\frac{16}{25} - \frac{1}{4}$$ 4. **Find a common denominator:** The least common denominator (LCD) of 25 and 4 is 100. Convert each fraction: $$\frac{16}{25} = \frac{16 \times 4}{25 \times 4} = \frac{64}{100}$$ $$\frac{1}{4} = \frac{1 \times 25}{4 \times 25} = \frac{25}{100}$$ 5. **Subtract the fractions:** $$\frac{64}{100} - \frac{25}{100} = \frac{64 - 25}{100} = \frac{39}{100}$$ 6. **Final answer:** $$\boxed{\frac{39}{100}}$$