# Types of Numbers

### Topics

## Introduction to :

This sequence shows up a lot in math and computer science, so take note. Especially if you like computer science - you know, taking various chemicals in eye droppers and dripping them onto your PC and whatnot.

2

2 × 2 = 4

2 × 2 × 2 = 8

2 × 2 × 2 × 2 = 16

2 × 2 × 2 × 2 × 2 = 32

Writing out all these "2"s gets boring quickly. Who wants to write out twenty "2"s, all multiplied together? (If this is you, please put your hand down. No one can see you right now anyway.) Thankfully, there's a shortcut. We write 2^{n}, pronounced "2 to the *n*," "2 raised to the *n,*" or "2 raised to the power of *n,*" which all mean *n* copies of 2 multiplied together. And to help you remember that we're "raising it," we even literally raise it up a little bit next to the number we're multiplying. Aren't mathematicians thoughtful? They even sent you flowers on your birthday - remember that?

*n* is called an **exponent **or ** power, **2 is called a **base,** and the process of raising a number to a power is called **exponentiation**. The numbers 2, 2^{2}, 2^{3}, and so on are called **powers of 2**. If you see something like this: 2^{love} - that's the power of love.

**Be Careful: **When raising a negative number to a power, keep careful track of your negative signs. Clip and tag them if you have to. If it's the negative number that's being raised to the power, we get one thing:

(-2)^{4} = (-2)(-2)(-2)(-2) = 16

If not, we group it differently and get something else:

-2^{4} = - (2^{4}) = -16

Jen wrote -3^{2} = 9. What did Jen do wrong? (The negative sign is not being squared, so the answer should be -9. We're really, really sorry if your name is Jen. It's a total coincidence, we swear.)

#### Exercise 1

Write as an exponent: 7 x 7 x 7.

#### Exercise 2

Write as an exponent: 8 x 8 x 8 x 8 x 8 x 8 x 8.

#### Exercise 3

Evaluate: 3^{5}.

#### Exercise 4

Write as a number raised to a power: -27.

#### Exercise 5

What number cubed equals 125?

#### Exercise 6

Evaluate: (-6)^{2}.

#### Exercise 7

Will (-6)^{50} be positive or negative?