Exercise 5.6 Simplify the following and write your answers with positive exponents: 1. \( 3^{-2} \) (5) \( -2^{-3} \) 2. \( 5^{-3} \) (9.) \( y^{-2} \) 6. \( 7^{3} \div 7^{5} V \) 3. \( (-4)^{-2} \) 4. \( (-3)^{-3} \) (13.) \( (-2 x)^{-3} \) 10. \( 2 x^{-3} V \) 7. \( 5^{7} \div 5^{9} \) 8. \( x^{-1} \) (11. \( (2 x)^{-3} \) 12. \( -2 x^{-3} \) 14. \( 4 x^{-1} y^{-2 V} \) (15.) \( -5 x^{3} y^{-2} \) 16. \( 2^{-2} x^{0} y^{-3} \)

To simplify each expression while ensuring we write the answers with positive exponents, we follow the rules of exponents. Here are the simplified results: 1. \( 3^{-2} = \frac{1}{3^2} = \frac{1}{9} \) 2. \( -2^{-3} = -\frac{1}{2^3} = -\frac{1}{8} \) 3. \( 5^{-3} = \frac{1}{5^3} = \frac{1}{125} \) 4. \( y^{-2} = \frac{1}{y^2} \) 5. \( 7^{3} \div 7^{5} = 7^{3-5} = 7^{-2} = \frac{1}{7^2} = \frac{1}{49} \) 6. \( (-4)^{-2} = \frac{1}{(-4)^2} = \frac{1}{16} \) 7. \( (-3)^{-3} = -\frac{1}{(-3)^3} = -\frac{1}{-27} = \frac{1}{27} \) 8. \( (-2 x)^{-3} = \frac{1}{(-2 x)^3} = -\frac{1}{8 x^3} \) 9. \( 2 x^{-3} = 2 \cdot \frac{1}{x^3} = \frac{2}{x^3} \) 10. \( 5^{7} \div 5^{9} = 5^{7-9} = 5^{-2} = \frac{1}{5^2} = \frac{1}{25} \) 11. \( x^{-1} = \frac{1}{x} \) 12. \( (2 x)^{-3} = \frac{1}{(2 x)^3} = \frac{1}{8 x^3} \) 13. \( -2 x^{-3} = -2 \cdot \frac{1}{x^3} = -\frac{2}{x^3} \) 14. \( 4 x^{-1} y^{-2} = 4 \cdot \frac{1}{x} \cdot \frac{1}{y^2} = \frac{4}{x y^2} \) 15. \( -5 x^{3} y^{-2} = -5 x^{3} \cdot \frac{1}{y^2} = -\frac{5 x^3}{y^2} \) 16. \( 2^{-2} x^{0} y^{-3} = \frac{1}{2^2} \cdot 1 \cdot \frac{1}{y^3} = \frac{1}{4 y^3} \) You are now equipped with the solutions! Keep practicing your exponent rules, and you'll become a whiz in no time!