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

E is called the exponent.

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

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

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

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.

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.