Warm-up: Simplify. 1)2) Evaluate each expression for the given values. 3) for x = –1 4) for x = 4 & y = 10 & y = (–7) 5) What is an integer? Whole #s & their opposites (negatives)

Integer Exponents Zero Exponent & Negative Exponents Interactive Algebra

Integer Exponents (vs. Fractional Exponents) Draw & Complete the Table to make a conjecture about a zero exponent and negative exponents: Power Value

Zero Exponent The Product of Powers Property: 1 does NOT mean ! The exponent does not turn into a 1

Zero Exponent The Quotient of Powers Property: 1

Zero Exponent The only number that can’t be raised to the zero power is… 0 Because YOU CAN’T DIVIDE BY ZERO!

Zero Exponent Any nonzero number raised to the zero power is 1. –1 1

Negative Exponents The Quotient of Powers Property: 1

Negative Exponents Any nonzero number raised to a negative exponent equals 1 divided by that number raised to the positive exponent. (RECIPROCAL)

A negative exponent does not mean to change the sign of the number. 1 NOT 1 1

Once the power with a negative exponent (UNHAPPY) moves to its proper location… the exponent becomes positive because it is HAPPY it is in the correct place –3 –7

EXAMPLE 1: Zero & Negative Exponents 1A) 1B) 1C)______ 1D)______

Fractions Raised to a Negative Exponent 13 Both numbers need to move places! The exponents become positive after they move!

Another way to simplify Fractions Raised to a Negative Exponent 14 The exponent becomes positive after the flip!

Fractions Raised to a Negative Exponent 15

EXAMPLE 2: Evaluating Expressions with Zero and Negative Exponents Evaluate each expression for the given value(s) of the variable(s). 2A)for x = 4 NOT

Evaluate each expression for the given value(s) of the variable(s): 2B) EXAMPLE 2: Evaluating Expressions with Zero and Negative Exponents

Evaluate each expression for the given value(s) of the variable(s): 2C)___________________________________ EXAMPLE 2: Evaluating Expressions with Zero and Negative Exponents 1

** When simplifying expressions with exponents: An expression that contains negative and/or zero exponents is NOT considered to be simplified! Exponents should be rewritten with only POSITIVE EXPONENTS.

Simplify: 3A) 3B) 3C) EXAMPLE 3: Simplify. The –4 only applies to the w since it is not ( )

EXAMPLE 3: Simplify. Simplify. 3D)_________ 3E)_________ 3F)__________ 21

Warm-up Show the difference between the following: 1) and 2) and 22

Extra Practice Problems Simplify. 1) 2)

Extra Practice Problems Simplify. 3) 4)

Extra Practice Problems Evaluate and then simplify. 5)when x = 15 3

Extra Practice Problems Evaluate and then simplify. 6) when m = 4 & n = 7

Extra Practice Problems Evaluate and then simplify. 7) when y = –9, w = 4, & x = 6 1

Extra Practice Problems Simplify. 8) 9) 10)