Algebra Demystified 2nd Ed

Chapter 5 e X P O N e N T S a N D r O O T S 125

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

4.^35
5

35

5

x 12 35 5 12

x

x

x

− xx

−

= −

−

=−− −

()

()()

5.^1
10

1

10

3 4 43 10 43

()()

()

x x

==x−

6. 22 xx^23 ()−=yx^23 ()xy−^2
   7.^38
   12 5

38

12 5

7 x^3373812537

x

x

x

+ xx

+

= +

+

=+ + −

()()

()()

8. x
   y

x

y

x

y

− 533 = − 5 = − (^3) =−xy 3 −
12
52
()() 12 52

9.^16
31

16

31

16

31

16

3

4

4 3

4

314

14

x 314

x

x

x

x

x

x

+

=

+

=

+

()=

()

()( 331 x+)−^14

10. ()
    ()

()

()

()

()

x (

x

x

x

x

x

− x

+

= −

+

= −

+

(^1) =−
1
1
1
1
1
4
(^53)
5 4
5 3
45
35 111
)(^45 x+)−^35

Simplifying Multiple Roots

The exponent-root properties are useful for simplifying multiple roots. With

the properties naam==mn/ and()aamn mn we can gradually rewrite the multiple

root as a single root. We rewrite each root as a power, one root at a time, and

then we multiply all of the exponents. This gives us an expression containing a

single exponent. Once we have the expression written with a single exponent,

we rewrite it as a root.

EXAMPLES

Write the expression as a single root.

45 x

We begin with^5 x.

(^45) xx==^415 //()xx^1514 /(==^15 /)(/^14 )/xx^120 =^20
(^63) yy^5 == 6 53 //()yy^5316 /(==^53 /)(/^16 )/y^518
EXAMPLES
Write the expression as a single root.
EXAMPLES
Write the expression as a single root.