Define and Use Zero and Negative Exponents

Goal • Use zero and negative exponents .

Your Notes

DEFINITION OF ZERO AND NEGATIVE EXPONENTS
Words	Algebra	Example
a to the zero power is 1.
a-n is the reciprocal of an.
an is the reciprocal of a-n.

Example 1 Use definition of zero and negative exponents

	pression s.html">Evaluate the expression .
In this lesson, when simplifying powers with numerical bases, evaluate the power.		Definition of negative exponents Evaluate exponent.
		Definition of zero exponent
		Definition of negative exponents
		Evaluate exponent.
		Simplify.
	undefined	a-n is defined only for a nonzero number a .

Your Notes

PROPERTIES OF EXPONENTS Let a and b be real numbers , and let m and n be integers.
	Product of powers property
	Power of a power property
	Power of a product property
	Quotient of powers property
	Power of a quotient property

Example 2 Evaluate exp onential expressions

Evaluate the expression.
	Product of powers property Add exponents. Definition of zero exponent
	Power of a power property Multiply exponents. Evaluate power.
	Definition of negative exponents Evaluate power.
	Quotient of powers property Subtract exponents. Evaluate power.

Your Notes
Guided Practice Evaluate the expression.

Example 3 Use properties of exponents

Simplify the expression Write your answer using only positive exponents . Solution
	Definition of negative exponents
	Power of a product property
	Product of powers property
	Quotient of powers property

Homework

Guided Practice Simplify the expression.