1. Simplify.     (a⁶b⁷)⁶

2. Simplify.  (y³/z⁵)⁵   

3. Classify the following as a monomial, binomial or trinomial, where possible. -(vw²/2)

4. Classify the following as a monomial, binomial or trinomial, where possible. 4x² - 3xy + y²

5. Classify the following as a monomial, binomial or trinomial, where possible. y⁷ + y⁶ + 8y⁵+ 2

6. Write in descending order and give the degree. 7x³ + 10x⁴ + 10

7. Evaluate -x² - 10x - 6 for x = 3.

8. True or False?     The degree of a trinomial is never 4.

9. Evaluate (assume x does not equal 0).   8x⁰

10. Write using positive exponents and simplify, if possible.    5^-3

11. Simplify and write your answer with only positive exponents. m⁵/m²⁰            

12. Simplify.  Write your answer with only positive exponents.     (r³)^-5/r(r³)^-4

13. Express the number in scientific notation.The diameter of Neptune: 49,600,000 m

14. Perform the indicated calculations.  Write your result in scientific notation. (8 x 10⁸)(5.4 x 10³)/(2.7 x 10¹⁴)(2 x 10¹⁵)

15. The distance from a star to a planet is 7.4 x 10¹⁸ m.  How long does it take light, traveling at 10¹⁶ m/year, to travel from the star to the planet?

16. Add 6m² - 2m - 4 and 10m² + 3m - 6.

17. Remove the parentheses and simplify.     7y - (-10y - 9x)

18. Subtract 4d² + 9d - 10 from 10d² - 3d + 7.

19. Perform the indicated operations.[(6y² + 2y - 2) - (-y² - 10y + 2)] - (-4y² + 3y + 3)

20. A census study shows that the population from 1990 to 1998 of the only large town in a certain county can be modeled by the formula 102t² - 225t + 3090 where t = 0 represents the year 1990 and that over the same years, the population of the surrounding county (not including the town) can be modeled by the formula 125t² + 72t + 4978 where t = 0 represents the year 1990.  Find a model for the total population of the county during the years 1990 to 1997.

21. Multiply.    -6x(-4x - 7)

22. Multiply.     (5m - 3)(4m + 7)

23. Multiply.     (-4x - 2)²

24. Divide.   50x³ - 70x²/10x

25. Divide.    x⁴ - 10x² +31/x²-5

26. Write 7.7x10^8 in standard notation.

27. Evaluate 4x^0+5

28. Simplify and write using positive exponents.(-6)^-2

29. Simplify x^-7/y^-2

30. Multiply (x-9)(x+9)