(2/3) 2÷(4/9) 2

To solve \((\frac{2}{3})^2 \div (\frac{4}{9})^2\), we will first calculate each term separately and then perform the division. 1. Calculate \((\frac{2}{3})^2\): \[ (\frac{2}{3})^2 = \frac{2^2}{3^2} = \frac{4}{9} \] 2. Calculate \((\frac{4}{9})^2\): \[ (\frac{4}{9})^2 = \frac{4^2}{9^2} = \frac{16}{81} \] 3. Now, substitute those results into the division: \[ \frac{4}{9} \div \frac{16}{81} \] 4. Dividing by a fraction is the same as multiplying by its reciprocal: \[ \frac{4}{9} \times \frac{81}{16} \] 5. Now, multiply the fractions: \[ = \frac{4 \times 81}{9 \times 16} \] 6. Simplify: \[ = \frac{324}{144} \] 7. Now, simplify \(\frac{324}{144}\): - Divide both the numerator and the denominator by their greatest common divisor, which is 36: \[ = \frac{324 \div 36}{144 \div 36} = \frac{9}{4} \] Thus, the final answer is: \[ \frac{9}{4} \]