Name ___________________________________________________ Date ________________ Hour ________

Standard G: Exponents

Lesson 1

Product & Quotient Rules

Warm-Up: Without the use of a calculator, evaluate the following expression given the value for

each variable in the expression. Your answer must be as simplified as possible.

√𝑥8𝑦5𝑥7

𝑥7𝑦6𝑧 given 𝑥 = 4, 𝑦 = 6, 𝑎𝑛𝑑 𝑧 = 2

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What is an exponent?

Name the parts of an exponential expression: 𝑎𝑏

Parentheses play a huge role in exponential expressions. If there are no parentheses in the expression,

you can only assume that an exponent applies to ___________________________________________. If

there are parentheses in the expression, you can assume that the exponent applies to

_________________________________________________.

For example, in 2𝑥𝑦3, to which base(s) does the exponent “3” apply?

In 2𝑥(6𝑦𝑏)4, to which base(s) does the exponent “4” apply?

When simplifying exponential expressions, you must always combine any bases that are the same

down to one base with a new exponent; this includes bases which are numbers. To finish simplifying,

any number bases must be expanded (for example, 23 must be written as 8).

Product Rule: If you multiply two (or more) exponential expressions with the same base, you must

____________ the exponents. The base will remain the same; only the exponent value will change.

Why? Write out the following exponential expression, and then simplify it down to one term.

(𝑥5)(𝑥4) =

Examples: Simplify each of the following exponential expressions.

1. (𝑥3)(𝑥4) = 2. (22)(23) =

3. (2𝑥2𝑦3𝑧)(23𝑥4𝑧2)= 4. (2𝑥2𝑎)(3𝑥3𝑎2)=

Quotient Rule: If you divide two (or more) exponential expressions with the same base (typically

written as a fraction), you must ______________ the exponents. The base will remain the same; only the

exponent value will change. Pay attention to whether there is more of the base in the numerator or

denominator in the beginning- this is where all of the remaining base will be.

Why? Write out the following exponential expression, and then simplify it down to one term.

𝑥7

𝑥3 = vs. 𝑥3

𝑥7 =

Examples: Simplify each of the following exponential expressions.

1. 105

102 = 2. 𝑥3𝑦2𝑧

𝑥𝑦5 =

3. 3𝑎4𝑏4𝑐4

6𝑎5𝑏2𝑐4= 4. 2𝑥2𝑎

23𝑥3𝑎2 =