Exponents

When a number is used as a repeated factor: , it can be written in exponential form, .

4 is the base: the number that is being multiplied

3 is the exponent: tells us how many times the base is being multiplied by itself

Examples:

(a)

(b)

(c)

(d)

Laws of Exponents

(1) Product Rule

This example illustrates:

Examples:

(a)

(b)

(2) Quotient Rule

This example illustrates:

Examples:

(a)

(b)

(3) Zero Exponent

or

Thus

This example illustrates

Examples:

(a)

(b)

(c)

(4) Negative Exponent

or

Thus

This example illustrates

Examples:

(a)

(b)

(5) Raising a Product to a Power

This example illustrates

Examples:

(a)

(b)

(6) Raising a Power to a Power

This example illustrates

Examples:

(a)

(b)

(7) Raising a Fraction to a Power

This example illustrates

Examples:

(a)

(b)

Problems

Simplify

(1) (6)

(2) (7)

(3) (8)

(4) (9)

(5) (10)

Answers

(1) (6) -1

(2) (7)

(3) (8)

(4) (9)

(5) 1 (10)