1. **State the problem:** Calculate the value of $$\left(\frac{4}{5}\right)^2 - \left(\frac{1}{2}\right)^2$$. 2. **Recall the formula:** To square a fraction, square the numerator and the denominator separately: $$\left(\frac{a}{b}\right)^2 = \frac{a^2}{b^2}$$. 3. **Calculate each square:** $$\left(\frac{4}{5}\right)^2 = \frac{4^2}{5^2} = \frac{16}{25}$$ $$\left(\frac{1}{2}\right)^2 = \frac{1^2}{2^2} = \frac{1}{4}$$ 4. **Subtract the two fractions:** $$\frac{16}{25} - \frac{1}{4}$$ 5. **Find a common denominator:** The least common denominator of 25 and 4 is 100. 6. **Rewrite each fraction with denominator 100:** $$\frac{16}{25} = \frac{16 \times 4}{25 \times 4} = \frac{64}{100}$$ $$\frac{1}{4} = \frac{1 \times 25}{4 \times 25} = \frac{25}{100}$$ 7. **Subtract the numerators:** $$\frac{64}{100} - \frac{25}{100} = \frac{64 - 25}{100} = \frac{39}{100}$$ 8. **Final answer:** $$\boxed{\frac{39}{100}}$$ This is the simplified result of the original expression.