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properties of radicals

0 votes

Using properties of radicals

Simplify the expression.

1)(256)1/3×(4)1/3

2)(16)1/3×(2)1/3

asked Oct 29, 2013 in ALGEBRA 2 by skylar Apprentice

1 Answer

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1) (256)1/3×(4)1/3

The expression is (256)1/3×(4)1/3

=(28)1/3×(22)1/3                               (22=4)(28=256)

The property(am)n =amn

=(2)8/3×(2)2/3                                  ((52)1/3 = (5)2/3 )

The property am×an=am+n

=(2)(8/3)+(2/3)                                      ( (8/3)+(2/3)=10/3=3.33)

=23.3                                                   

=23.3

(256)1 /3×(4)1/3=23.3.

2)(16)1/3×(2)1/3

The expression is (16)1/3×(2)1/3

= (24)1/3×(2)1/3                           (16 = 24)

The property(am)n =amn

= (2)4/3×(2)1/3                            ((24)1/3 = (2)4/3)

The property am×an=am+n

= (2)(4/3)+(1/3)                                ((2)4/3×(2)1/3 = (2)(4/3)+(1/3))

= 2(5/3)                                         ((4/3)+(1/3)=5/3)  

= ( 25)1/3

= (32)1/3

(16)1/3×(2)1/3 = (32)1/3.

answered Oct 29, 2013 by rob Pupil

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