# Mixed Algebra and Exponent Problems

Here are some practice problems that I have done and am trying to self check

Please complete all the problems on the attached document using Microsoft word's equation editor. Please see the attached file.

Thanks

1. Write each expression with positive exponents only and then simplify:

a. 2 -1 + 4 -1

b. ( 2/5 ) -3

2. Add or subtract as indicated:

a. ( - 6X3 + 7 X2 - 9X + 3) + (14X3 + 3X2 -11X -7)

b. (13X4 - 8X3 + 2X2 ) - ( 5X4 -3X3 + 2X2 -6)

3. Find each product:

a. 3y2 (-7y2 + 3y -6)

b. (3y -2 ) ( 4y2 + 3y -5 )

4. Divide:

a. 40 X8 Y6

5 XY3

b. X3 -2X2 -33X -7

X -7

5. Simplify each expression:

a. ( -10 )0

b. 400X0

6. Write each number in scientific notation:

a. 73, 900, 000

b. 0.38

7. Factor by grouping:

a. X3 + 3X2 + 2X + 6

b. XY + 4X - 2Y - 8

8. Factor completely:

a. X2 -X -20

b. 12y3 + 28y2 + 8y

9. Factor completely or state that it is "Prime":

a. Z4 -16

b. X2 + 1

10. Factor Completely:

a. X2 -16X + 64

b. X3 - 27

11. Solve each equation:

a. X(X -12 ) = 0

b. 5X2 +20X = 0

12. The length of a rectangular sign is 3feet longer than the width. If the sign has a area of 40 square feet for advertising, find its length and its width.

13. Find all the numbers for which the rational expression is undefined:

a. X + 3

(X -2 )(X + 5)

b. 7

X2 + 81

14. Simplify

a. X2 - 4

X - 2

b. y2 + 2y

y2 + 4y + 4

15. Multiply or divide as indicated:

a. 5X + 5 multiplied by 3X

6 X2 + X

b. X2 + X divided by 2X + 4

10 5

16. Add or Subtract as indicated, Simplify the results, if possible:

a. 7 + 4

(X + 3) (X + 3)2

b. 6y - 3

y2 - 4 y + 2

17. Solve each irrational equation. If an equation has no solution, so state:

a. 3 - 1 = 1

X 6 X

b. 13 - 3 = 1

y - 1 y - 1

18. A car travels 60 miles in the same time that a car traveling 10 per hour faster travels 90 miles. What is the rate of each cars?

19. Find the indicated root or state that the expression is not a real number:

a. 3√ 8

125

This is the cube root of 8/125.

b. -4√81

20. Simplify each expression:

a. √45X23

b. √ 96

3

21. Add or subtract as indicated:

a. 4√72 - 2√48

b. √75 - √48

22. Multiply as indicated:

a. (√11 - √ 5 ) (√11 +√ 5)

b. ( 1 + √2) 2

23. Solve each radical expression:

a. √ (2X - 1) = X - 2 This the square root of what is in the parenthesis.

b. √3X + 5 = 11 This is the square root of 3x

24. Simplify:

a. 64 2/3

b. (-8 ) -4/3

25. Solve by completing the square:

X2 -12X + 27 = 0

26. Solve by using the quadratic formula:

X2 = 2X + 4

27. Solve each equation:

a. X2 = -100

b. 5X2 = -125

Given the parabola y = x2 - 6x -7 , answer the following questions:

28. Determine if the parabola whose equation is given opens upward or downward. What is its x-intercept?

29. Find its y-intercept. What are the coordinates of the vertex?

30. Graph the parabola.

#### Solution Summary

This includes problems on a variety of topics - scientific notation, factoring, simplifying exponents, solving irrational equations, and radicals.