# Honors Algebra 2: Extra Practice on Integral Exponents with Addition

• Class: Honors Algebra 2
• Author: Peter Atlas
• Algebra and Trigonometry: Structure and Method, Brown

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1. $$\displaystyle \frac{(x + y)^{-2}}{(x + y)^{-1}}$$
2. Solution

$$\displaystyle \frac{1}{x + y}$$

3. $$\displaystyle \frac{a^{-1} - b^{-1}}{a^{-1} + b^{-1}}$$
4. Solution

$$\displaystyle \frac{b - a}{b + a}$$

5. $$\displaystyle (z - w)\left(w^{-1} - z^{-1}\right)$$
6. Solution

$$\displaystyle \frac{w^2 - 2wz + z^2}{wz}$$

7. $$\displaystyle \left(d^{-1} + e^{-1}\right)(d + e)^{-1}$$
8. Solution

$$\displaystyle \frac{1}{de}$$

9. $$\displaystyle \left(x^{-1} + y^{-1}\right)^{-2}$$
10. Solution

$$\displaystyle \frac{x^2y^2}{\left(x + y\right)^2}$$

11. $$\displaystyle \left(x^{-1} + x^{-2}\right)^{-1}$$
12. Solution

$$\displaystyle \frac{x^2}{x + 1}$$

13. $$\displaystyle \left(x^{-1} - x^{-2}\right)(x - 1)^{-1}$$
14. Solution

$$\displaystyle \frac{1}{x^2}$$

15. $$\displaystyle (x + y)^{-2}\left(x^{-2} - y^{-2}\right)^{-1}$$
16. Solution

$$\displaystyle \frac{x^2 y^2}{(x+y)^3 (y-x)}$$

17. $$\displaystyle \left(2^{-2} + 3^{-3}\right)^{-1}$$
18. Solution

$$\displaystyle \frac{108}{31}$$

19. $$\displaystyle \left(2x^{-1} + 3x^{-2}\right)^{-1}$$
20. Solution

$$\displaystyle \frac{x^2}{2x + 3}$$