# Honors Algebra 2: Extra Practice on Positive and Negative Exponents

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

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1. $$\displaystyle \left( -7u^{2}\right) \left( 5u^{8}\right)$$
2. Solution

$$-35u^{10}$$

3. $$\displaystyle \left( -8v^{3}\right) \left( -6v^{-9}\right)$$
4. Solution

$$\displaystyle \frac{ 48}{v^{6}}$$

5. $$\displaystyle \left( 2x^{4}y^{-7}\right) \left( 3x^{-1}y^{5}\right)$$
6. Solution

$$\displaystyle \frac{6x^{3}}{y^{2}}$$

7. $$\displaystyle \left( 9z^{6}w^{8}\right) \left( -5z^{-6}w^{-11}\right)$$
8. Solution

$$\displaystyle -\frac{45}{w^{3}}$$

9. $$\displaystyle \left( 5a^{-3}a^{-2}b^{-1}\right) \left( -25a^{6}b^{-4}\right)$$
10. Solution

$$\displaystyle -\frac{125a}{b^{5}}$$

11. $$\displaystyle \left( -3p^{4}q^{-3}\right) ^{2} \left( 4p^{-5}q^{7}\right)$$
12. Solution

$$36p^{3}q$$

13. $$\displaystyle \left( \frac{3}{4} d^{3}e^{-5}\right) ^{-2}$$
14. Solution

$$\displaystyle \frac{16e^{10}}{9d^{6}}$$

15. $$\displaystyle \left( \frac{1}{2} a^{2}b^{3}\right) ^{4} \left( a^{-5}b^{-10}\right)$$
16. Solution

$$\displaystyle \frac{a^{3}b^{2}}{16}$$

17. $$\displaystyle \left( 6x^{8}y^{-9}\right) \left( x^{-2}y^{-3}\right) ^{3}$$
18. Solution

$$\displaystyle \frac{6x^{2}}{y^{18}}$$

19. $$\displaystyle \left( -v^{7}w^{-8}\right) ^{3} \left( -v^{-9}w^{6}\right) ^{4}$$
20. Solution

$$\displaystyle -\frac{1}{v^{15}}$$

21. $$\displaystyle \left( u^{6}\right) ^{-4} \left( u^{3}\right) ^{8}$$
22. Solution

$$1$$

23. $$\displaystyle \left( ab\right) ^{-7} \left( a^{3}b^{-2}\right) ^{4}$$
24. Solution

$$\displaystyle \frac{a^{5}}{b^{15}}$$

25. $$\displaystyle \frac{c^{4}d^{-3}}{c^{3}d}$$
26. Solution

$$\displaystyle \frac{c}{d^{4}}$$

27. $$\displaystyle \left( \frac{f^{5}g^{-3}}{g^{-5}}\right) ^{2}$$
28. Solution

$$f^{10}g^{4}$$

29. $$\displaystyle \frac{\left( 2r^{3}s^{-3} \right) ^{5}}{ \left( 4r^{7}s^{-10}\right)}$$
30. Solution

$$\displaystyle \frac{8r^{8}}{s^{5}}$$

31. $$\displaystyle \frac{25x^{-5}y^{3}}{ \left( 5x^{2}y\right) ^{-3}}$$
32. Solution

$$3125xy^{6}$$

33. $$\displaystyle \left( \frac{3u^{-4}v^{3}}{ 2u^{-5}v} \right) ^{-2}$$
34. Solution

$$\displaystyle \frac{4}{9u^{2}v^{4}}$$

35. $$\displaystyle \left( - \frac{a^{-2}b^{-1}}{3a^{-3}b^{3}} \right) ^{-4}$$
36. Solution

$$\displaystyle \frac{81b^{16}}{a^{4}}$$

37. $$\displaystyle \frac{a^{m + 1}}{a^{m - 1}}$$
38. Solution

$$a^{2}$$

39. $$\displaystyle \left( b^{2 - p}b^{2+p}\right) ^{2}$$
40. Solution

$$b^{8}$$

41. $$\displaystyle 5 \left( 5^{e+1}\right) ^{e-1}$$
42. Solution

$$5^{e^2}$$