Power
Initial Definition

A power of a base "B" is any expression in the form BE.

E is called the exponent.

Example One

24 = 2 x 2 x 2 x 2.

24 = (2)(2)(2)(2).

24 = 16

Base: 2

Exponent: 4

Expanded Form: 2 x 2 x 2 x 2    or    (2)(2)(2)(2).

Standard Form: 16

Example Two

In the term  3(-2)5,   3 is a coefficient, (-2)5 is a power.

(-2)5 = -2 x -2 x -2 x -2 x -2.

(-2)5 = (-2)(-2)(-2)(-2)(-2).

(-2)5 = -32

3(-2)5 = 3 x -2 x -2 x -2 x -2 x -2.

3(-2)5 = (3)(-2)(-2)(-2)(-2)(-2).

3(-2)5 = -96

Coefficient: 3

Base: -2

Exponent: 5

Expanded Form: 3 x -2 x -2 x -2 x -2 x -2    or    (3)(-2)(-2)(-2)(-2)(-2).

Standard Form: -96

Example Three

In the term  5x4,   5 is a numerical coefficient, x4 is a power.

x4 = (x)(x)(x)(x).

5x4 = (5)(x)(x)(x)(x).

Numerical Coefficient: 5

Base: x

Exponent: 4

More

It is important to be able to distinguish between terms like  (-2)4  and terms like  -24. Note that is this case  (-2)4 ≠ -24.

Convention

If a base is written without an exponent, the exponent is one.

• 3 = 31.
• a = a1.
• -3 = (-3)1.    [Note: brackets are important.]
• 4x3yx2 = 41x3y1x2.

Demonstration Image only

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