**Exponents** **Practice Questions**

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

Tips and Shortcuts Common Exponents Tests with Exponents

Practice Questions Answer Key Tutorials

**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 2. (The answer is 750).

- 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).

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 School** – BC Provincial, COOP, HSPT, ISEE, SHSAT, SSAT, TACHS,

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

**High School Equivalency:** CHSPE, GED

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

a. 123

b. 1.23

c. 0.0123

d. 0.00123

e. 0.000123

1. A

2. C

3. E

4. E

5. C

6. C

7. A

Purple Math – Simple Rules for Exponents

Introduction to Exponents -Video

**Written by:** **Modified: ** August 18th, 2018 August 18th, 2018**Published: ** March 27th, 2013

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.