114 algebra De mystif ieD

DeMYSTiFieD / algebra DeMYSTiFieD / HuttenMuller / 000-0 / Chapter 5

EXAMPLES

Rewrite using Property 10.

64 =⋅=⋅ 416416 =⋅= 248

(^5534) xx= (^512)
(^464) xy (^44) = 24 xy
still struggling
Property 10 only applies to multiplication. There is no similar property for addi-
tion (nor subtraction). a common mistake is to “simplify” the sum of two squares.
For example, xx^2 +=+ 93 is incorrect. The following example should give you
an idea of why these two expressions are not equal. If there were the property
nab+= +nnab, then we would have 58 =+ 49 94 =+ 99 =+= 7310. This
could only be true if 10^2 = 58, which of course, it isn’t.

?

Property 11 a

b

a

b

n

n

=n

Property 11 allows us to take the quotient followed by the root or the individual

roots followed by the quotient.

EXAMPLE

4

9

4

9

2

3

==

Property 12 naa

m n m

()= (Remember that if n is even, then a must not be

negative.)

By Property 12, we can take the root followed by the power or the power

followed by the root, as in 553

3

=().

Property 13 naaa

n n n

()==

We can think of Property 13 as a root-power cancellation property. We will use

this property later to simplify expressions involving a root and, in later chapters,

to solve equations.

EXAMPLES

Rewrite using Property 10.

EXAMPLES

Rewrite using Property 10.

EXAMPLEEXAMPLE