182 Rational Numbers

Perform Operations with Exponents

Simplify x^3 · x-^5.

Method 1 Product of Powers

x^3 · x-^5 = x^3 + (-5)

(^) = x- 2
Method 2 Definition of Power
x^3 · x-^5
= x · x · x · x · x · x^1 · x · x
= x^1 · x^1 · x^1 · x^1
1 ·^ x 1 ·^ x 1 ·^ x^ ·^ x
= x^1 · x or x-^2
Simplify
g^5

g^2
.
Method 1 Quotient of Powers
g^5

g^2
= g^5 -^2
(^) = g 3
Method 2 Definition of Power
g^5

g^2

g^1 · g^1 · g^1 · g · g
__
g^1 · g^1
= g^3
e. x

• 2
  _
  x-^1

f. c-^4 · c^3

WATER A molecule of water contains two hydrogen atoms and

one oxygen atom. A hydrogen atom is only 0.00000001 centimeter

in diameter. Write the decimal as a power of ten.

The digit 1 is in the 100-millionths place.

0.00000001 = _^1

100,000,000

Write the decimal as a fraction.

= _^1

108

100,000,000 = 108

= 10 -^8 Definition of negative exponent

A hydrogen atom is 10-^8 centimeter in diameter.

g. MEASUREMENT A unit of measure called a micron equals

0.001 millimeter. Write this number using a negative

exponent.

Real-World Link

A single drop of water

contains about 10^20

molecules.

RR

A

176_189_C3L4_895130.indd 182 12/31/09 12:50 PM