Evaluate this exponential expression 27/8^ 4/3 a. 9/2 b. 4/3 c. 81/16

81/16

Step-by-step explanation:

This expression  27/8^ 4/3 is best written as

  27

( )^(4/3)

    8

Noting that both 27 and 8 are perfect cubes, we rewrite this expression as

  27

[ ( )^(1/3) ] ^4

    8

Note how 27^(1/3) = ∛27 = 3 and 8^(1/3) = ∛8 = 2, so we obtain:

     3

[ ( ) ] ^4

      2

This can be left as is, or rewritten as

     3^4              81

[ ( ) ]  =  

      2^4             16

b is the correct answer