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Types of Numbers

Types of Numbers

At a Glance - Exponents and Powers - Whole Numbers

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 2s gets boring quickly. Who wants to write out twenty 2s, 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 2n, pronounced "2 to the n," "2 raised to the n," or "2 to the nth power," 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?

If we've got 2n, that little n is called an exponent or power, 2 is called the base, and the process of raising a number to a power is called exponentiation. The numbers 2, 22, 23, and so on are called powers of 2. If you see something like 2love, 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:

-24 = -(24) = -16

Sample Problem

Jen wrote -32 = 9. What did Jen do wrong?

The negative sign isn't being squared, so the answer should be -9. It would only be positive 9 if we had (-3)2. We're really, really sorry if your name is Jen. It's a total coincidence, we swear.

Example 1

What is 3 × 3 × 3 × 3 in exponential terms?


Example 2

Evaluate 53.


Exercise 1

How do we rewrite 7 × 7 × 7 in exponential terms?


Exercise 2

How do we rewrite 8 × 8 × 8 × 8 × 8 × 8 × 8 in exponential terms?


Exercise 3

What is 35?


Exercise 4

Write -27 as a number raised to the 3rd power.


Exercise 5

What number cubed equals 125?


Exercise 6

Evaluate: (-6)2.


Exercise 7

Will (-6)50 be positive or negative?


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