Practice with Exponents Topic Index | Algebra Index | Regents Exam Prep Center

Test your skills on the following problems:

 1. Rewrite the following expression without using exponents:    84 Answer The exponent is 4. The base is 8. So there are 4 eights being multiplied together. So,   (8)(8)(8)(8)

 2. Which of the following is equal to the expression:                                            3-7 Choose one: 37 (-3)7 Answer A negative exponent is the same as 1 over the base to the positive exponent.

 3. What is the value of the expression:                                  (-2)3(3)2 ? -72   72 -36 Answer The expression is the same as (-2)(-2)(-2)(3)(3) which equals (-8) times (9) = -72. So, a is correct.

 4. Which of the following has a value of 1 ? (-1)2 1-1 10 all of the above Answer All of these equal 1. a)  (-1)(-1) = 1 b)  1/1  = 1 c)  any number to the 0  equals 1. So, d is correct.

 5. The expression  (30)(40)(22) is equal to: 4 1 0 none of the above Answer 3 to the 0 = 1 4 to the 0 = 1 2 to the 2 = 4 1 times 1 times 4 = 4 So, a is correct.

Now let's investigate a situation involving exponents:

 6. Computers store information with electrical components that are either "on" or "off".  Each component stores a bit, which has a value of either 1 (on) or 0 (off).  Such a process uses the binary number system, or the base 2 number system.  Remember that our decimal system (base 10) represents numbers as powers of ten:                     units (100), tens (101), hundreds (102), thousands (103) and so on. The binary system works in the same way with a base value of 2. a.  What is the value represented by each place in a binary number?  (Fill in the blanks.)       ______    ______   ______   ______   ______   ______   ______   ______           27              26           25          24           23          22          21           20        Answer 2^0 = 1 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 2^7 = 128 b.  What is the decimal value of the binary number  10111 ?  (If a 1 appears, you are to add the value of that place holding to the total value of the number.) Answer 10111 base 2 = 23 base 10 ANSWER: 23 c.   Eight bits, as shown in part a, comprise a byte.  If all of the bits in a byte were "turned on" (1), what is the largest decimal value that can be stored in one byte (8 bits)?    Answer The sum would be the sum of 1 times the value of each place. 128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 = 255 ANSWER: 255

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