32. Zero exponent. Simplify each expression.
5y^2z(y^-3z^-1)

38. Changing the sign of an exponent. Write each expression without negative exponents and simplify.
5^-2xy^-3
3x^-2

52. The quotient rule for exponents. Simplify each expression.
2r^-3t^-1
10r^5t^2∙t^-3

64. Use the rules of exponents to simplify each expression.
2x^2∙5y^-5

72. For each equation find the integer that can be used as the exponent to make the equation correct.
1 over 125 = 5?

84. Scientific notation. Write each number in standard notation.
48 x 10^-3

90. Write each number in scientific notation.
8,200,100

96. Evaluate each expression using scientific notation without a calculator.
(6000)(0.00004)
(30,000)(0.002)

16. Raising an exponential expression to a power.
Assume the variablesrepresent nonzero real numbers and use positive exponents only in your answer.
(m^-3)^-1(m^2)^-4

26. Raising a product to a power. Simplify.
(2x^-1y^2)^-3

36. Raising a quotient to a power.
(2a^2b)^-3
3

44. Simplify.
(-2/3)^-2

54. Variable exponents. Simplify each expression. Assume that the variables represent integers.
(5^4^-3y)^3(5^y^-2)^2

64. Summary of rules. Use the rules of exponents to simplify each expression if possible.
(-2y^4)^3
X

72. Use the rules of exponents to simplify each expression.
(3x^-1y^3)^-2 over (3xy^-1)^3 (9x^-9y^5)
NOTE THE LAST SET OF PARENTHESES ARE NEXT TO THE FIRST AND SECOND SET OF PARENTHESES

80. Write each expression as 2 raised to a power. Assume that the variables represent integers.
6^n^-5∙3^5^-n

Please see the attached file for the fully formatted problems.
1. Convert the following equations into logarithmic form:
a. 9 = 4x
b. 3 = 6y
c. 5 = 7y
d. X = 9y
2. Convert the following equations into exponential form:
a. X = log3 6
b. -5 = log3 y
c. X = log4 y
d. 1000 = log5 Z

Differential Equation (IX): Formation of Differential Equations by Elimination
Eliminate the arbitrary constants from the equation: y = Ae^x + Be^2x + Ce^3x. Make sure to show all of the steps which are involved.

What are the steps for simplifying radicals? Can either step be deleted? If you could add a step that might make simplifying radicals easier or easier to understand, what step would you add?

1. Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Show your work. Use the resulting ordered pairs to plot the graph. State the equation of the line asymptotic to the graph (if any).
y = 3x - 4
2. Evaluate the logarithmic equation for three values of x that

1. Complex Exponentials: Simply the following expression and give your answer both in polar and rectangular form.
o c=3ejπ/4+4e−jπ/2
2. Difference Equations: Solve the following difference equation using recursion by hand (for n=0 to n=4)
o y[n] + 0.5y[n-1] = 2x[n-1]; x[n] = δ[n], y[-1] = 0
3. Differential Equations

Please provide an answer to the questions below that contains 250 to 300 words to each.
1.If a < b, then -a > -b, Why? Illustrate your reasoning with several examples.
2.How can you differentiate between an equation and an expression? Give several examples of each.
3.How does the knowledge of simplifying an express