1. Simplify the following expressions:

      3 3 -3 3    6 6
 a. (x y x  y )/(x y )

    (x x x)(x x x)
 b. --------------
         x³

    (y^-3)(x^-6)
 c. ------------
      (xy)^-4

 d. [(xyz) ³ / (z⁴y²x)](z²)⁶

 e. x²x³x⁴x⁵x⁶x⁷x^-15

    ((x x x x x) + (x x x x))x
 f. --------------------------
         (1 /(x^-3))²

              2    -2
 g. (x(y + z)) (xyz)

2. Solve the following (or simplify)

 a. M = log(283)         b. M = log_10(283³²)

 c. M = log_5(283)       d. M = log_5(1415/5)

 e. M = log(10³6 ² )       f. M = log_10(xy/z)

                                    6x(y ²)(z^-2)
 g. M = log_16((a/2)⁴)  h. M = log(-------------)
                                         Pi

3. What happens if you try to solve the following using your caculator?

 a. M = log_10(-2)       b. M = log_10(0)

4. What are the following values when written in scientific notation?

 a. 1,003,000,000,000,000,000,000,000

 b. (3.695)¹⁵

 c. (3.695 x 10¹⁵)

 d. (1.38)^-9

5. Solve the following equation by simplifying x, y and z with scientific notation first:

 x = 0.00000000000000000008
 y = 0.0000000000045
 z = 10,880,200,000,000,000,000

       x (y³)² z
 M = [------------]²
       (xy)^(1/2)

6. Convert the following binary values into base 10 values:

 a. 1010        b. 1111        c. 0

 d. 1101011010  e. 1110100011  f. 11111111111111

7. Convert the following base 10 values into base 2, binary:

 a. 192         b. 1,253       c. 69

 d. 85          e. 16,530      f. 16

8. Use what you have learned to:

 a. Similar to the binary table you use for converting between binary and decimal, make a table for converting base 5 numbers to base 10 numbers, showing the exponent value for the first 6 places.

 b. convert 281, a base 10 number, to a base 5 value.

 c. Convert 1341404, a base 5 number, to a base 10 number.

Used with permission of the Author; Copyright (C) Kevin A. Shaffer 1998 - 2022, all rights reserved.