Exponents

Definition: If n is a positive integer

n factors of a

Examples:

4³ = (4)(4)(4)

(-3)² = (-3)(-3). The square of negative three.

-3² = -(3)(3). The negative of the square of three.

(2x)² = (2x)(2x) = 4x². The square of 2x.

2x² = 2(x)(x). Twice the square of x.

Laws of Exponents:

Motivational example:

Note to multiply exponential expressions with the same base you add the exponents on the factors to obtain the exponent on the answer.

Law I:

Motivational example:

Note when raising an exponential expression to a power we multiply the exponents together to obrain the exponent on the answer.

Law II:

Motivational example:

Note when raising a product to a power we raise each factor to the power.

Law III:

Motivational example:

Note when dividing exponential expressions with the same base we subtract the exponent on the denominator from the exponent on the numerator.

Law IV:

Motivational example:

Note when raising a quotient to a power we raise the numerator to the power and divide by the denominator raised to the power.

Law V:

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