EXPONENT RULES Exponent Definition: Part A: Product Rule 1. Simplify 42•43 2. Simplify x2•x3 Hint: Rewrite the terms in expanded form: x2 = ___________ and x3 = __________ How many x’s are there? Rewrite your answer with exponents: _____________________________ 3. Now simplify x4•x8 4. x?•x5 = x11 ? = __________ Now look at your answers in Part A. What do you observe? Write a rule explaining what you did. Part B: Power Rule 1. Simplify (43)2 2. Simplify (x3)2 Hint: Rewrite the term in expanded form: x3 = ___________ Now if we square it, what does that mean? (xxx)(xxx) Rewrite your answer with exponents: _____________________________ 3. Now simplify (x8)5 4. (x?)5 = x30 ? = __________ Now look at your answers in Part B. What do you observe? Write a rule explaining what you did. EXPONENT RULES Part C: Quotient Rule 𝑥3 1. Simplify 𝑥 5 Hint: Rewrite the terms in expanded form, and reduce common factors How many x’s are left? Are they in the numerator or denominator? Rewrite your answer with exponents: _____________________________ 2. What stays in the numerator if all the factors “cancel out”? 3. Simplify 4. Simplify 𝑥7 𝑥5 𝑥 11 𝑥? = 𝑥2 ? = __________ Now look at your answers in Part C. What do you observe? Write a rule explaining what you did. Part D: Negative Exponents Rule 1. Simplify 3 − 7 Is your answer positive or negative? 2. Look back at Part C, if you use the Division Rule to simplify 𝑥3 𝑥7 , is the x4 in the numerator or denominator? 3. What does this tell you about negative exponents? 4. Simplify x-6 using only positive exponents 1 5. Simplify 𝑥 −7 using only positive exponents Now look at your answers in Part D. What do you observe? Write a rule explaining what you did. EXPONENT RULES Part E: Parentheses: Distributing Exponents THIS RULE ONLY WORKS IF THERE IS MULTIPLICATION OR DIVISION IN THE PARENTHESES. If the parentheses contain addition or subtraction, DO NOT APPLY THIS RULE 1. Write (2𝑥)3 in expanded form: ____________________ 2. Simplify the expression in #1: _______________________ 𝑥 4 3. Write (5) in expanded form: ___________________ 4. Simplify the expression in #3. When there is a product or quotient in parentheses, you can _______________________ the exponent. Part F: Zero Exponents Anything raised to the zero power = _____ Use the following pattern to figure out the zero exponent rule: 23 = 22 = 21 = 20 = 2−1 = 2−2 =