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# Knowledge is POWER! Learning about powers and their properties.

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Author: Nate Muckley
##### Description:

This packet teaches the definitions, uses, and properties of powers.

This packet goes over the basic information about powers. The BASICALLY AWESOME information about powers, that is!

On a more serious note, though...

The packet also teaches the Power of a Power property, Product of Powers property, and Power of a Product property.

This videos give examples, and the pictures are very clear, colorful, and easy to understand.

(more)
Tutorial

## A few definitions...

A POWER is an expression that denotes a number multiplied by itself many times.  This sounds complicated, but is really quite easy.

They are written like this:

32

There are two parts of a power, the BASE--

3

and the EXPONENT

2

A power signifies that the base is multiplied by itself the number of times in the exponent, so...

32 = 3 x 3

(you multiply 3 two times)

This equals 9

--------------------------------------------------------

25 = 2 x 2 x 2 x 2 x 2

(you multiply 2 five times)

This equals 32

-------------------------------------------

What is 42?

## Properties

Powers have 3 important properties:

Product of Powers

When a power is multiplied to a power with the same base, the answer has the base raised to the power of the exponents added together.

am x an = a(m+n)

Here's why:

42 x 43

well, 42 = 4 x 4                  and 43 = 4 x 4 x 4

put together, it's 4 x 4 x 4 x 4 x 4

or

4

[ 2 + 3 = 5 ]

Power of a Power

When a power is raised to a power, the answer has the base with the two powers multiplied together.

(am)n = a(mn)

Here's why:

(64)2

well, 64 = 6 x 6 x 6 x 6,  and since they are squared, it can be represented by:

(6 x 6 x 6 x 6) x (6 x 6 x 6 x 6) OR 6 x 6 x 6 x 6 x 6 x 6 x 6 x 6

Simply

68

[ 4 x 2 = 8]

Power of a Product

When the base of a power has multiple terms multiplied together, the exponent gets distributed to all of the terms.

(ab)m = am x bm

Here's why:

(2Y)3

Well, (2Y)3 = (2 x 2 x 2) x (Y x Y x Y)

(23) x (Y3)

Without parentheses:

2x Y3

Check out the videos and diagrams below to see these properties in action!

## Product of Powers!

Learn how to use the Product of Powers property.

## Power of a Power

Learn how to use the Power of a Power property. Narrated by Rachel Kaplan.

## Power of a Product ## Using Power of a Product Rating Header