Laws of Exponents

Exponential Notation Base Exponent Base raised to an exponent

Goal To write simplified statements that contain distinct bases, one whole number in the numerator and one in the denominator, and no negative exponents. Ex:

Description of Lesson This power point will address the laws of exponents in the following manner: 1.Explore how the rule works. 2.State the rule. 3.Provide an example with a solution. 4.Provide extra examples (Find me to get solutions)

Exploration Evaluate the following without a calculator: 3 4 = 3 3 = 3 2 = 3 1 = Describe a pattern and find the answer for: 3 0 = ÷ 3

Zero Power Anything to the zero power is one Can “a” equal zero? a 0 = 1 No. You can’t divide by 0.

Exploration Simplify:

Product of a Power If you multiply powers having the same base, add the exponents.

Example Simplify:

Practice Simplify the following expressions:

Exploration Simplify:

Power of a Power To find a power of a power, multiply the exponents.

Example Simplify:

Practice Simplify the following expressions:

Exploration Simplify:

Power of a Product If a base has a product, raise each factor to the power

Example Simplify:

Practice Simplify the following expressions:

Negative Powers A simplified expression has no negative exponents.

Example Simplify:

Example Simplify:

Practice Simplify the following expressions:

Exploration Simplify:

Quotient of a Power To find a quotient of a power, subtract the bottom exponent from the top if the bases are the same.

Example Simplify:

Practice Simplify the following expressions:

Exploration Simplify:

To find a power of a quotient, raise the denominator and numerator to the same power. Power of a Quotient

Example Simplify:

Practice Simplify the following expressions: