Chapter 5 e X P O N e N T S a N D r O O T S 109DeMYSTiFieD / algebra DeMYSTiFieD / HuttenMuller / 000-0 / Chapter 5- ()
x
x
+
− =−
82
43- ()x
y
+
=−
−3 2 −
43✔SOLUTIONS
- (xy^3 )^2 = x^2 (y^3 )^2 = x^2 y^6
- ()
()
3 1
31
31
273x xx (^3333) x
− ===
- (2x)^4 = 24 x^4 = 16 x^4
- (3(x − 4))^2 = 32 (x − 4)^2 = 9(x − 4)^2
- 6(2x)^3 = 6(2^3 x^3 ) = 6(8x^3 ) = 48 x^3
- 6y^2 (3y^4 )^2 = 6 y^2 (3^2 (y^4 )^2 ) = 6 y^2 (9y^8 ) = 54 y^10
- (5x^2 y^4 z^6 )^2 = 52 (x^2 )^2 (y^4 )^2 (z^6 )^2 = 25 x^4 y^8 z^12
8.^44264
(^33)
yy^23 y^6
==()
9.^2
9
9
29
8(^33)
3
3
x
xx
−
= − = −
− ()()
- () ()
[( )] ()
x
xx
xx
x +
= + = +8 −
882
4(^343)
23
12
6
- () [( )]
()
x ()()
yx
y + x
= + = +−
−− −−
−−332 3 −
4(^323)
43
2 (()
()()
− ()
−− =
(^3) +
43
6
12
3
y
x
y
Multiplying/Dividing with Exponents
When multiplying (or dividing) quantities that have exponents, we use expo-
nent properties to simplify each factor (or numerator and denominator) and
then we multiply (or divide).