Power

Initial Definition

Example One

2^{4} = 2 x 2 x 2 x 2.

2^{4} = (2)(2)(2)(2).

2^{4} = 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 5x^{4}, 5 is a numerical coefficient, x^{4} is a power.

x^{4} = (x)(x)(x)(x).

5x^{4} = (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 -2^{4}.

Note that is this case (-2)^{4} ≠ -2^{4}.

Convention

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

- 3 = 3
^{1}. - a = a
^{1}. - -3 = (-3)
^{1}. [Note: brackets are important.] - 4x
^{3}yx^{2}= 4^{1}x^{3}y^{1}x^{2}.

Demonstration

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Instructions text as in global.js