Evaluate each expression: 1. (3/5)³, 2. (-7)⁴, 3. (9/4) × (2/3)², 4. 2 (7/9) ÷ (−1 (2/3))², 5. (−2/5)² × (−5/2)³, 6. (−2)⁴ + (−3)³, 7. (0.3)² × 3⁻².

Steps to Solve

1. Calculate (3/5)³
   Raise the fraction to the power of three:
   $$ \left(\frac{3}{5}\right)^3 = \frac{3^3}{5^3} = \frac{27}{125} $$

2. Calculate (-7)⁴
   Raise -7 to the power of four:
   $$ (-7)^4 = 7^4 = 2401 $$

3. Calculate (9/4) × (2/3)²
   First, calculate $(2/3)²$ and then multiply:
   $$ (2/3)^2 = \frac{2^2}{3^2} = \frac{4}{9} $$
   Then multiply:
   $$ \frac{9}{4} \times \frac{4}{9} = 1 $$

4. Calculate 2 (7/9) ÷ (−1 (2/3))²
   First, find $(−1 \cdot (2/3))²$:
   $$ (-1 \cdot \frac{2}{3})^2 = \left(-\frac{2}{3}\right)^2 = \frac{4}{9} $$
   Then divide:
   $$ 2 \cdot \frac{7}{9} \div \frac{4}{9} = 2 \cdot \frac{7}{9} \times \frac{9}{4} = \frac{14}{4} = \frac{7}{2} $$

5. Calculate (−2/5)² × (−5/2)³
   Calculate each part separately:
   $$ (-\frac{2}{5})^2 = \frac{4}{25} $$
   $$ (-\frac{5}{2})^3 = -\frac{125}{8} $$
   Then multiply:
   $$ \frac{4}{25} \times -\frac{125}{8} = -\frac{500}{200} = -\frac{5}{2} $$

6. Calculate (−2)⁴ + (−3)³
   First, calculate each term:
   $$ (-2)^4 = 16 $$
   $$ (-3)^3 = -27 $$
   Then add:
   $$ 16 - 27 = -11 $$

7. Calculate (0.3)² × 3⁻²
   First, calculate $(0.3)²$:
   $$ (0.3)^2 = 0.09 $$
   Next, calculate $3^{-2}$:
   $$ 3^{-2} = \frac{1}{3^2} = \frac{1}{9} $$
   Then multiply:
   $$ 0.09 \times \frac{1}{9} = 0.01 $$