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**Exponents And Powers - Whole Numbers**: At a Glance

- Topics At a Glance
- Different Types of Numbers
- Natural Numbers
- Whole Numbers
- Integers and Negative Numbers
- Integers and Absolute Value
- Rational Numbers
- Irrational Numbers
- Real Numbers and Imaginary Numbers
- Different Ways to Represent Numbers
- Fractions
- Equivalent Fractions
- Mixed Numbers
- Reducing Fractions
- Comparing Fractions
- Least Common Denominator
- Addition and Subtraction of Fractions
- Multiplication of Fractions
- Equivalent Fractions and Multiplication by 1
- Multiplication by Clever Form of 1
- Multiplicative Inverses
- Division of Fractions
- Multiplication and Division with Mixed Numbers
- Decimals
- Converting Fractions into Decimals
- Converting Decimals into Fractions
- Comparing Decimals
- Adding and Subtracting Decimals
- Multiplication and Division by Powers of 10
- Multiplying Decimals
- Dividing Decimals
- Infinite Decimals
- Percents
- Portion of the Whole
**Things to Do with Real Numbers**- Addition and Subtraction of Real Numbers
- Properties of Addition
- Subtraction
- Multiplication
- Division
- Long Division Remainder
**Exponents and Powers - Whole Numbers**- Properties of Exponents
- Prime Factorization
- Order of Operations
- Even and Odd Numbers
- Infinity
- Sequences
- is Irrational
- Counting Rational Numbers
- Counting Real Numbers?
- Counting Irrational Numbers
- In the Real World
- Decimals in Use
- How to Solve a Math Problem
- I Like Abstract Things: Summary

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.)

Example 1

Write 3 x 3 x 3 x 3 as an exponent. |

Example 2

Evaluate 5 |

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?