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properties of radicals

0 votes

Using properties of radicals

Simplify the expression.

1)(5)1/3×(25)1/3

2)(3)1/4×(27)1/4

3)(64)1/2×(4)1/2

asked Oct 29, 2013 in ALGEBRA 2 by linda Scholar

1 Answer

0 votes

1) The expression is (5)1/3×(25)1/3

=(5)1/3×(52)1/3                                     (52=25)

The property(am)n =amn

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

The property am×an=am+n

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

=51                                            

=5

(5)1/3×(25)1/3 =5

2) (3)1/4×(27)1/4

The expression is (3)1/4×(27)1/4

=(3)1/4×(27)1/4                           (33=27)

The property(am)n =amn

=(3)1/4×(3)3/4                             (  (33)1/4 = (3)3/4 )

The property am×an=am+n

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

= 31

=3

(3)1/4×(27)1/4 = 3.

3) (64)1/2×(4)1/2

The expression is  (64)1/2×(4)1/2  

=(43)1/2×(4)1/2

The property(am)n =amn

=(4)3/2   Ã—(4)1/2

The property am×an=am+n

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

=(4)2                            

=16

(64)1/2×(4)1/2 = 16.

answered Oct 29, 2013 by casacop Expert

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