MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Simplify the expression. Write the answer using only positive exponents. Assume that all variables represent positive real numbers.

1) (mn^{-13})(m^{-6}n^{6})

A) m^{5}n^{7}

B) (1/m^{5}n^{7})

C) (m^{5}/n^{7})

D) (1/m^{6}n^{7})

2) (3x^{5}y^{5})^{3}(x^{7}y^{2})^{-4}

A) (y^{7}/27x^{13})

B) 27x^{13}y^{7}

C) (27/x^{13}y^{7})

D) (27y^{7}/x^{13})

3) 15^{0} – (-12)^{0}

A) 2

B) 27

C) -2

D) 0

4) ((3xy^{3}z^{-2})^{2}/(4x^{5}yz^{-4})^{-1})

A) (36x^{7}y^{7}/z^{8})

B) (36y^{7}/x^{4}z^{8})

C) – (9y^{7}/4x^{3}z^{8})

D) – (9x^{7}y^{7}/4z^{8})

5) (a^{3}b^{-3}/2a^{-2}b^{4})^{-5}

A) (32b^{35}/a^{5})

B) (32b^{35}/a^{25})

C) (b^{35}/32a^{25})

D) (a^{25}/32b^{35})

6) (4x^{-3}y^{9}z)^{5}(4x^{-1}y^{8}z)^{-6}

A) (4/x^{9}y^{3}z)

B) (4x^{9}z/y^{3})

C) (4z/x^{9}y^{3})

D) (1/4x^{9}y^{3}z)

Add or subtract as indicated.

7) (8x^{4} – 9x^{3} + 8x^{2} + 7x + 4) + (-4x^{4} + 6x^{3} + 3x^{2} – 6x – 6)

A) 12x^{4} – 15x^{3} + 5x^{2} – x + 10

B) 4x^{4} – 3x^{3} + 11x^{2} + x – 2

C) 4x^{4} – 15x^{3} + 5x^{2} + x + 10

D) 12x^{4} – 15x^{3} + 5x^{2} – x – 2

8) (9y^{5} + 6y^{4} + 6y^{3} – 9) – (6y^{5} – 8y^{3} – 9y^{4} – 8)

A) 15y^{5} – 3y^{4} – 2y^{3} – 17

B) 3y^{5} – 3y^{4} – 2y^{3} – 17

C) 15y^{5} – 3y^{4} – 2y^{3} – 1

D) 3y^{5} + 15y^{4} + 14y^{3} – 1

9) Add.

4ab^{3} – 2a^{2}b^{2} – 2b^{5}

6ab^{3} – 6a^{2}b^{2} – 2b^{5}

A) 10ab^{3} – 8a^{2}b^{2}

B) 10ab^{3} – 8a^{2}b^{2} – 2b^{5}

C) 10ab^{3} – 8a^{2}b^{2} + 4b^{5}

D) 10ab^{3} – 8a^{2}b^{2} – 4b^{5}

10) Subtract.

3x^{8} + 9x^{7} – 5x^{6} + 1

8x^{8} – 6x^{7} + 9x^{6} + 2

A) 11x^{8} + 3x^{7} + 4x^{6} – 1

B) 11x^{8} + 3x^{7} + 4x^{6} + 3

C) -5x^{8} + 3x^{7} + 4x^{6} + 3

D) -5x^{8} + 15x^{7} – 14x^{6} – 1

Find the product.

11) (2x – 12)(x – 6)

A) 2x^{2} – 25x + 72

B) x^{2} – 24x – 25

C) 2x^{2} – 24x + 72

D) x^{2} + 72x – 24

12) (-5a + 7)(-5a – 2)

A) 25a^{2} + 25a – 14

B) 25a^{2} – 14

C) 25a^{2} + 45a – 14

D) 25a^{2} – 25a – 14

13) (12p + 5)(12p – 5)

A) 144p^{2} + 120p – 25

B) 144p^{2} – 120p – 25

C) p^{2} – 25

D) 144p^{2} – 25

14) (9y^{2} + 13)(9y^{2} – 13)

A) 81y^{2} – 169

B) 81y^{4} – 234y^{2} – 169

C) 81y^{4} – 169

D) 81y^{4} + 234y^{2} – 169

15) (10a^{3} + 9c)(10a^{3} – 9c)

A) 100a^{6} + 180a^{3}c – 81c^{2}

B) 100a^{6} – 180a^{3}c – 81c^{2}

C) 10a^{6} – 9c^{2}

D) 100a^{6} – 81c^{2}

16) (2m + 11)^{2}

A) 4m^{2} + 121

B) 2m^{2} + 44m + 121

C) 2m^{2} + 121

D) 4m^{2} + 44m + 121

17) (2a – 7)^{2}

A) 2a^{2} + 49

B) 4a^{2} + 49

C) 4a^{2} – 28a + 49

D) 2a^{2} – 28a + 49

18) (9x + 2y)^{2}

A) 81x^{2} + 36xy + 4y^{2}

B) 9x^{2} + 4y^{2}

C) 81x^{2} + 4y^{2}

D) 9x^{2} + 36xy + 4y^{2}

19) (10x – 9y)^{2}

A) 100x^{2} – 180xy + 81y^{2}

B) 100x^{2} + 81y^{2}

C) 10x^{2} + 81y^{2}

D) 10x^{2} – 180xy + 81y^{2}

20) (x + 3y)(x^{2} – 3xy + 9y^{2})

A) x^{3} – 27y^{3}

B) x^{3} + 27y^{3}

C) x^{3} + 6x^{2}y^{2} + 6xy + 27y^{3}

D) x^{3} – 6x^{2}y^{2} – 6xy + 27y^{3}

21) (7p – 1)(49p^{2} + 7p + 1)

A) 343p^{3} + 1

B) 343p^{3} + 56p^{2} – 1

C) 49p^{3} – 1

D) 343p^{3} – 1

Factor the polynomial completely.

22) 56x^{8}y^{8} – 40x^{2}y^{5} + 32x^{6}y^{2}

A) 8x^{2}(7x^{6}y^{8} – 5y^{5} + 4x^{4}y^{2})

B) 8x^{2}y^{2}(7x^{6}y^{6} – 5y^{3} + 4x^{4})

C) 8(7x^{8}y^{8} – 5x^{2}y^{5} + 4x^{6}y^{2})

D) x^{2}y^{2}(56x^{6}y^{6} – 40y^{3} + 32x^{4})

23) x^{2} – x – 30

A) (x + 1)(x – 11)

B) (x + 5)(x – 6)

C) (x – 6)(x + 6)

D) (x + 6)(x – 5)

24) 5x^{2} – 19x – 4

A) (5x + 4)(x – 1)

B) (5x + 1)(x – 4)

C) (5x – 4)(x + 1)

D) (5x – 1)(x + 4)

25) 36x^{2} – 25

A) (36x + 1)(x – 25)

B) (6x – 5)^{2}

C) (6x + 5)(6x – 5)

D) (6x + 5)^{2}

26) 81x^{2} – 144x + 64

A) (81x + 1)(x + 64)

B) (9x – 8)^{2}

C) (9x – 8)(9x + 8)

D) (9x + 8)^{2}

27) 25x^{2}z – 40xyz + 16y^{2}z

A) (5xz – 4yz)^{2}

B) z(5x + 4y)^{2}

C) z(5x – 4y)^{2}

D) z(5x – 4y)(5x + 4y)

28) x^{3} – 1,000

A) (x – 10)(x^{2} + 10x + 100)

B) (x – 10)(x^{2} + 100)

C) (x + 10)(x^{2} – 10x + 100)

D) (x + 1,000)(x^{2} – 1)

29) 343c^{3} + 125

A) (7c – 5)(49c^{2} + 35c + 25)

B) (7c + 5)(49c^{2} – 35c + 25)

C) (7c + 5)(49c^{2} + 25)

D) (343c + 5)(c^{2} – 35c + 25)

30) 25p^{6} – 64

A) (5p^{3} + 8)^{2}

B) (5p^{3} + 8)(5p^{3} – 8)

C) (5p^{3} – 8)^{2}

D) 25p^{6} – 64

31) 8am + 48mb + 7an + 42nb

A) (8m + n)(a + 42b)

B) (8m + 7n)(a + 6b)

C) (8m + 6b)(a + 7n)

D) (a + 7n)(8m + 6b)

32) x^{4} – 81

A) Prime

B) (x + 3)^{2}(x – 3)^{2}

C) (x^{2} – 9)(x + 3)(x – 3)

D) (x^{2} + 9)(x + 3)(x – 3)

33) 4k^{2} – 12kp + 9p^{2} – 1

A) (2k – 3p – 1)^{2}

B) (2k + 3p + 1)(2k + 3p – 1)

C) (2k – 3p + 1)(2k – 3p – 1)

D) (2k + 3p + 1)(2k – 3p – 1)

34) 6x^{2} – 21x – 12

A) 3(2x – 1)(x + 4)

B) (2x – 1)(3x + 12)

C) 3(2x + 1)(x – 4)

D) (6x – 3)(x + 4)

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