110 algebra De mystif ieD
DeMYSTiFieD / algebra DeMYSTiFieD / HuttenMuller / 000-0 / Chapter 5EXAMPLE
Simplify the expression.
3 x^3 (4xy^5 )^2
We begin by simplifying the quantity inside the parentheses, (4xy^5 )^2.
[4^2 x^2 (y^5 )^2 ] = (16x^2 y^10 ), so3 x^3 (4xy^5 )^2 = 3 x^3 [4^2 x^2 (y^5 )^2 ] = 3 x^3 (16x^2 y^10 ) = 3 · 16x^3 x^2 y^10 = 48 x^5 y^10(2x)^3 (3x^3 y)^2 = (2^3 x^3 )(3^2 (x^3 )^2 y^2 ) = (8x^3 )(9x^6 y^2 ) = 8 · 9x^3 x^6 y^2 = 72 x^9 y^2()
()5 ()()
105
10125
100(^3231)
2
33323
22
96
2
xy
x
xy
x
xy
x
===^225
100
5
4
5
4
xy^92 −^67 ==xy^6 xy^76
() 64 xy^42 ()xy^83 −−==(( 6422 xy^42 ))((^33 xy−−^83 ))( 36 x^2 yyxy
xxyy xy
8324
23824116
1
64
36
64
9
16
) −−
−− −−
====⋅⋅=^9
16
11 9
xy^1616 xy^16
PRACTICE
Simplify the expression.
- x
y
x
y3
2^52
=−- ()
()
2
6354
532xy
xy=- (2x^3 )^2 (3x−1)^3 =
- (3xy^4 )−2(12x^2 y)^2 =
- (4x−1y−2)^2 (2x^4 y^5 )^3 =
- ()
()
5
15433
52xy
xy=- ()
()
9
6232
23xy
xy−
=- [9(x + 3)^2 ]^2 [2(x + 3)]^3 =
- (2xy^2 z^4 )^4 (3x −1z^2 )^3 (xy^5 z−4) =
10.^2
3
43 24
4()()
()xy yz
xyz=EXAMPLE
Simplify the expression.EXAMPLE
Simplify the expression.PRACTICE
Simplify the expression.PRACTICE
Simplify the expression.