# mat 110 beginning algebra 0

1. Simplify. (*a*^{6}*b*^{7})^{6}

2. Simplify.

3. Classify the following as a monomial, binomial or trinomial, where possible.

4. Classify the following as a monomial, binomial or trinomial, where possible.

4*x*^{2} – 3*xy* + *y*^{2}

5. Classify the following as a monomial, binomial or trinomial, where possible.

*y*^{7} + *y*^{6} + 8*y*^{5}+ 2

6. Write in descending order and give the degree. 7*x*^{3} + 10*x*^{4} + 10

7. Evaluate –*x*^{2} – 10*x *– 6 for *x* = 3.

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

9. Evaluate (assume *x* does not equal 0). 8*x*^{0}

10. Write using positive exponents and simplify, if possible. 5^{–3}

11. Simplify and write your answer with only positive exponents.

12. Simplify. Write your answer with only positive exponents.

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.

15. The distance from a star to a planet is 7.4 · 10^{18} m. How long does it take light, traveling at 10^{16} m/year, to travel from the star to the planet?

16. Add 6*m*^{2} – 2*m* – 4 and 10*m*^{2} + 3*m *– 6.

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

18. Subtract 4*d*^{2} + 9*d* – 10 from 10*d*^{2} – 3*d *+ 7.

19. Perform the indicated operations. [(6*y*^{2} + 2*y* – 2) – (–*y*^{2} – 10*y* + 2)] – (–4*y*^{2} + 3*y* + 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 102*t*^{2} – 225*t* + 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 125*t*^{2} + 72*t* + 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. –6*x*(–4*x* – 7)

22. Multiply. (5*m* – 3)(4*m* + 7)

23. Multiply. (–4*x* – 2)^{2}

24. Divide.

25. Divide.

26. Write 7.7×10^8 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)

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