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

Knowledge is POWER! Learning about powers and their properties.

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)
See More

Try Our College Algebra Course. For FREE.

Sophia’s self-paced online courses are a great way to save time and money as you earn credits eligible for transfer to over 2,000 colleges and universities.*

Begin Free Trial
No credit card required

25 Sophia partners guarantee credit transfer.

221 Institutions have accepted or given pre-approval for credit transfer.

* The American Council on Education's College Credit Recommendation Service (ACE Credit®) has evaluated and recommended college credit for 20 of Sophia’s online courses. More than 2,000 colleges and universities consider ACE CREDIT recommendations in determining the applicability to their course and degree programs.

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