Question 1:

Perform the indicated operations and simplify.

(y-6)/(y-8) - (y+1)/(y+8) + (y-40)/(y²-64) =  ____

Question 2:

Solve.

6x⁴ - 17x² + 5 = 0

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A The solution is x= ____.
(Simplify your answer. Type an exact answer, using radicals as needed. Rationalize all denominators. Use a comma to separate answers as needed.)

B There is no solution.

Question 3:

Divide and simplify.

C³/c¹⁸ = ___ (Type exponential notation with positive exponents.)

Question 4:

Factor completely.

9x⁷ - 81x⁶ + 27x⁵

The complete factorization is ___. (Type your answer in factored form.)

Question 5:

Find the following. Assume that variables can represent any real number.

√(a+4)² = ___

Question 6:

Multiply and simplify. Assume variables represent nonzero real numbers.

c18.c⁰ =___ (Simplify your answer. Type exponential notation with positive exponents.)

Question 7:

Factor the trinomial.

a³ - 4a² - 45a

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. a³ - 4a² - 45a = ____(Factor completely.)

B. The trinomial is not factorable.

Question 8:

Divide.

(28b³ + 27b² + 26b + 47)/(4b + 5)

Choose the correct answer.
A. 7b² - 2b - 9 - (2/(4b+5))

B. 7b² - 2b + 9 + (2/(4b+5))

C. 7b²+ 2b + 9

D. 7b + 9

Question 9:

Solve.

5/v = 8/v-1/5

Select the correct choice below and, if necessary, fill in the answer box to complete 5 8 I your choice.

A. The solution is ___
(Simplify your answer. Type an integer or a fraction.)

B. The equation has no solution.

Question 10:

Multiply and simplify by factoring. Assume that all expressions under radicals represent nonnegative numbers.

³√(y⁴) ³√(81y⁵) = ____ (Simplify your answer. Type in radical form.)

Question 11:

Use rational exponents to write x^1/6 .y^1/7.z^1/4 as a single radical expression.

Choose the correct expression below.

A. ⁸⁴√(x¹⁴y¹²z²¹)

B. ⁸⁴√(xyz)

C. ⁸⁴√(xyz)⁴⁷

D ¹⁶⁸√(xyz)

Question 12:

Convert to decimal notaion.

8.04 x 10⁷ =___

Question 13:

Find the variation constant and an equation of variation where y varies directly as x and y= 70 when x= 10.

The variation constant is k = ____

The equation of variation is y=  ____

Question 14:

Simplify by removing factors of 1.

(s²-64)/(s + 8)²

The simplified form is ___.

Question 15:

Multiply.
(- 4t)²(3t⁴)²

(-4t)²(3t⁴)² = ___

Question 16:

Multiply.

(4√6 - 8√5) (5√6 + 10√5) = ___(Simplify your answer. Type an exact answer, using radicals as needed.)

Question 17:

Rewrite the following expression with positive exponents.
(35xy)^-7/9

Choose the correct equivalent expression