Exponents Practice Questions and Tutorial

Exponents are an essential part of basic math and appear on almost every high school exam and college entrance exam.

Exponents:  Tips, Shortcuts & Tricks

Exponents may seem like advanced math —like some mysterious code with a complicated meaning. In fact, though, an exponent is just short hand for saying that you’re multiplying a number by itself two or more times. For instance, instead of saying that you’re multiplying 5 x 5 x 5, you can show that you’re multiplying 5 by itself 3 times if you just write 53 .We usually say this as “five to the third power” or “five to the power of three.” In this example, the raised 3 is an “exponent,” while the 5 is the “base.”

You can even use exponents with fractions. For instance, ½ 3 means you’re multiplying ½ x ½ x ½. (The answer is 1/8). Some other helpful hints for working with exponents:

  • Here’s how to do basic multiplication of exponents. If you have the same number with a different exponent (For instance 53 X 52  ) just add the exponents and multiply the bases as usual. The answer, then, is 255 .
  • This doesn’t work, though, if the bases are different. For instance, in 53  X 32   we simply have to do the math the long way to figure out the final solution: 5 x 5 x 5,  multiplying that result times the result for 3 X 3. (The answer is 1125).
  • Looking at it from the opposite side, to divide two exponents with the same base (or bottom number), subtract the smaller exponent from the larger one. If we were dividing the problem above, we would subtract the 2 from the 3 to get 1.  5 to the power of 1 is simply 5.
  • One time when thinking of exponents as merely multiplication doesn’t work is when the raised number is zero. Any number raised to the “zeroth” power is 1 (Not, as we tend to think, zero).

Common Exponents

 

Number ( x ) Square ( x 2 ) Cube ( x 3 )
1 1 1
2 4 8
3 9 27
4 16 64
5 25 125
6 36 216
7 49
8 64
9 81
10 100
11 121
12 144
13 169
14 196
15 225
16 256

Standardized Tests with Exponents Questions

High SchoolBC ProvincialCOOP,  HSPT, ISEE, SHSAT, SSAT, TACHS,

Nursing Entrance: DET, NET, TEAS, PAX RN, PSB,

High School Equivalency: CHSPE, GED

Armed Services: AFQT, ASVAB

How to Study for a Math test

Practice Questions

1. 23 =

a. 8
b. 16
c. 32
d. 5

2. x5/x3=

a. x2
b. x-2
c. x8
d. x-8
e. x-1.6

3. 1002 x 1005 = 100y y=?

a. 1
b. 1.5
c. 2
d. 2.5
e. 7

4. Divide 0.123 by 103

a. 123
b. 1.23
c. 0.0123
d. 0.00123
e. 0.000123

5. 33 =

a. 1/81
b. 81
c. 27
d. 81

6.
exponents_clip_image012

a. -1
b. 0
c. 1
d. X-1

7. Multiple 104 by 102 

a. 108
b. 102
c. 106
d. 10-2

Answer Key

1. A

2. A
To divide exponents with the same base – subtract the exponents

3. E

4. E

5. C

6. C

7. C
To multiple exponents with the same base – add the exponents.

Written by:

    18 Comments

  1. Marcus
    December 28, 2014
    Reply

    how close is this to the actual HOAE test

    • Complete Test Prep
      December 30, 2014
      Reply

      The PSB HOAE test has exponents as part of the math section – these are for skills practice only.

  2. Tina
    January 11, 2016
    Reply

    nevermind. I figured it out. 1/0.125 is 1000/125=8. Math is my nemesis.. uggh.

  3. Mrs. Edwards
    April 10, 2016
    Reply

    Hello, I am looking for a good math book that teaches all the basic fundamentals of math for an adult (myself). I dropped out of high school so I missed out on learning percentage, fractions, etc. I now find math to be very intimidating. I probably need to start from the beginning so everything makes sense as I progress.

    If you can recommend a book that also has worksheets to practice that would be lovely.

    Thanking you in advance,
    Mrs. Edwards

  4. Complete Test Prep
    June 30, 2016
    Reply

    The answer is correct

    3. 1002 x 1005 = 100y y=

    When multiplying exponents of the same base, add them – y = 7

  5. Harlee
    May 5, 2017
    Reply

    Hi i have a question. Are you allowed to use a calulator when taking the hoae test?

    • Brian
      May 5, 2017
      Reply

      Hi – no calculators are not allowed on the PSB – see the PSB HOAE FAQ

  6. shaquerra jackson
    July 10, 2018
    Reply

    Can you explain number 2 and 6 please . Thanks

    • Nikki
      August 8, 2018
      Reply

      2) when u have exponents that are divided you need to subtract those exponents. So it is 5 – (-3). Subtracting a negative you change the sign. Change the -3 sign into positive, and the problem then becomes 5 + 3 which is 8. x to the 8th power is the answer which is c.

      • A
        July 11, 2019
        Reply

        What about #6 though?

      • s
        July 26, 2019
        Reply

        Yes but the question was x^5 * x^3 not -3….

  7. j
    May 16, 2019
    Reply

    explain #6?

  8. Chris Goins
    June 25, 2019
    Reply

    For some reason, super-scripted exponents are ending up displaying as subscript on my browser, and my fiance’s browser. Since exponents are superscripted, I thought I should make you aware. It’s very confusing!

    • Brian Stocker
      June 25, 2019
      Reply

      Many thanks! corrected!

  9. A
    July 11, 2019
    Reply

    Do you get a calculator on the SHSAT? Can you use a pencil? And can someone explain #6 to me? I got it wrong and I don’t know why.

    • Brian Stocker
      July 12, 2019
      Reply

      No calculators are not allowed on the SHSAT – See SHSAT FAQ

  10. Shahzaib Aftab
    July 27, 2019
    Reply

    Hello Sir, Please check Answer of Ques no.2. isnt it (C) the correct option

    • Aya
      November 7, 2019
      Reply

      no because when dividing with exponents, you subtract while, multiplying with exponents, you add them together so the answer would be (A).

Leave A Reply

Your email address will not be published. Required fields are marked *