# 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

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

7. Multiple 104 by 102

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

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.

### Exponents Tutorials

Written by: 1. December 28, 2014

how close is this to the actual HOAE test

• December 30, 2014

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

2. January 11, 2016

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

3. April 10, 2016

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.

Mrs. Edwards

4. June 30, 2016

3. 1002 x 1005 = 100y y=

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

5. May 5, 2017

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

• May 5, 2017

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

6. July 10, 2018

Can you explain number 2 and 6 please . Thanks

• August 8, 2018

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.

• July 11, 2019

• July 26, 2019

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

7. May 16, 2019

explain #6?

8. June 25, 2019

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!

• June 25, 2019

Many thanks! corrected!

9. July 11, 2019

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.

• July 12, 2019

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

10. July 27, 2019
• 