Knowledge is POWER! Learning about powers and their properties.

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

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2⁵ = 2 x 2 x 2 x 2 x 2

(you multiply 2 five times)

This equals 32

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What is 4²?

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.

a^m 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

4⁵ 

[ 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.

(a^m)^{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 = a^m x b^m

Here's why:

(2Y)³

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

(2³) x (Y³)

Without parentheses:

2³ x Y³

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