P2: Properties of Exponents

WARM UP – Copy the table below into your notes. Expand each problem and then simplify. RuleEx:ExpandedSimplifiedRule Product 2▪2 X 2▪2▪2=2525 Quotient Zero Exponent Negative Exponent Power to a power Power of a Product Power of a quotient

PRACTICE – identify which rule applies and simplify (don’t need to expand) (4x 3 y 4 )(10x 2 y 6 )

Practicing with Negative Exponents

Put it all together and what to you got??? Ex #7 SIMPLIFY:

THE END! HW: pg. 28 #1 – 35 eoo, 37 – 63 odd

A Natural Number Exponent If b is a real number and n is a natural number, b n is read “the nth power of b” or “ b to the nth power.” Thus, the nth power of b is defined as the product of n factors of b. Furthermore, b 1 = b

OH YEAH!!! CHEESY VIDEO TIME: Song: More serious tutorial video you can watch at home if you get stuck:

The Product Rule b m · b n = b m+n When multiplying exponential expressions with the same base, add the exponents. YOU TRY: a b. (4x 3 y 4 )(10x 2 y 6 ) Ex #1

The Quotient Rule When dividing exponential expressions with the same nonzero base, subtract the exponent in the denominator from the exponent in the numerator. Ex #2

The Quotient Rule explains Zero as an Exponent Any nonzero base raised to the power of “0” equals 1 b 0 = 1 Ex #2

Negative Exponents Cross the line to change the sign of the exponent. Ex #3

The Product Rule explains Powers to Powers When an exponential expression is raised to a power, multiply the exponents. (b m ) n = b mn Ex #4

Products to Powers When a product is raised to the power, raise each factor to that power. (ab n ) = a n b n Ex #5

Quotients to Powers When a quotient is raised to a power, raise the numerator to that power and divide by the denominator to that power. Both the numerator and the denominator are raised to that power. Ex #6

PRODUCT QUOTIENT ZERO & NEGATIVE PROPERTIES OF EXPONENTS (Graphical Organizer) Multiplying same bases Power to a power Power of a product Dividing same bases Power of a quotient Any nonzero number raised to the “0” power = 1 How do negative exponents become positive?