Copyright © 2011 Pearson Education, Inc.

Integral Exponents and Scientific Notation

Section P.2

Prerequisites

Copyright © 2011 Pearson Education, Inc. Slide P-3

P.2

Definition: Negative Integral ExponentsIf a is a nonzero real number and n is a positive integer, then

Rules of Negative Exponents and FractionsIf a and b are nonzero real numbers and m and n are integers, then

.1n

n

aa

.andn

m

m

nnn

ab

ba

ab

ba

Negative Integral Exponents

Copyright © 2011 Pearson Education, Inc. Slide P-4

P.2

If m and n are any positive integers, we have

This equation indicates that the product of exponential

expressions with the same base is obtained by adding

the exponents.

This fact is called the product rule.

.factors

factorsfactors

nm

nm

nm

nm aaaaaaaaa

Rules of Exponents

Copyright © 2011 Pearson Education, Inc. Slide P-5

P.2

Definition: Zero ExponentIf a is a nonzero real number, then a0 = 1.

Rules for Integral ExponentsIf a and b are nonzero real numbers and m and n are integers, then1. Product rule

2. Quotient rule

3. Power of a power rule4. Power of a product rule

5. Power of a quotient rule

nmnm aaa

nmn

m

aaa

nmnm aa )(nnn baba )(

n

nn

ba

ba

Rules of Exponents

Copyright © 2011 Pearson Education, Inc. Slide P-6

P.2

In scientific notation, a positive number is written as a

product of a number between 1 and 10 and a power of

10.

To convert from scientific notation to standard notation

multiply by the indicated power of 10.

Scientific Notation