# Exponents Practice Questions and Tutorial

- Posted by Brian Stocker MA
- Date Published March 27, 2013
- Date modified February 8, 2020
- Comments 20 comments

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

### Audio Version of this Post

### 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 5^{3} .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 5
^{3}X 5^{2}) just add the exponents and multiply the bases as usual. The answer, then, is 25^{5}. - This doesn’t work, though, if the bases are different. For instance, in 5
^{3}X 3^{2 }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 |

### Multiply and Dividing Exponents

### Practice Questions

**1. 2 ^{3} =**

a. 8

b. 16

c. 3^{2}

d. 5

**2. x ^{5}/x^{3}**=

a. x^{2}

b. x^{-2}

c. x^{8}

d. x^{-8}

e. x^{-1.6}

**3. 100 ^{2} x 100^{5} = 100^{y }y=?**

a. 1

b. 1.5

c. 2

d. 2.5

e. 7

**4. Divide 0.123 by 10 ^{3}**

a. 123

b. 1.23

c. 0.0123

d. 0.00123

e. 0.000123

**5. 3 ^{3} =**

a. 1/81

b. 81

c. 27

d. 81

a. -1

b. 0

c. 1

d. X-1

**7. Multiple 10 ^{4} by 10^{2} **

a. 10^{8}

b. 10^{2}

c. 10^{6 }

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

multiplying exponents – if the bases are the same then add the exponents – so -5 + 5 = 0 and -3 + 3 = 0 which gives x^{0} / x^{0} and any number raised to the power of 1 is 1, so 1/1 = 1

7. C

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

### Exponents Tutorials

**Written by:**Brian Stocker MA, Complete Test Preparation Inc.

Tag:Basic Math, Exponents

## 20 Comments

how close is this to the actual HOAE test

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

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

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

The answer is correct

3. 100

^{2}x 100^{5}= 100^{y}y=When multiplying exponents of the same base, add them – y = 7

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

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

Can you explain number 2 and 6 please . Thanks

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.

What about #6 though?

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

explain #6?

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!

Many thanks! corrected!

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.

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

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

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

How is the answer to question 6, C. 1? If you subtract -3 from -5 you get -2. If you subtract 3 from 5 you get 2. -2 plus 2 equals 0, not 1.

see my explanation in the answer key