16^5/4•16^1/4 / (16^1/2) ^2

The simplified expression is 16^-1/6

Step-by-step explanation:.

16^5/4•16^1 / 4 / (16^1/2) ^2

The dot means multiplication. The expression is rewritten as

16^5/4 * 16^1/4 / (16^1/2) ^2

Recall the following rules of indices

1) y^a * y^b = y^ (a+b)

2) (y^a) ^b = y^ab

y^b / y^a = y^ (b-a)

Applying these rules of indices

16^5/4 * 16^1/4 = 16^ ((5/4*1/4) = 16^ ((5/16)

(16^1/2) ^2 = 16^ 1/2*2 = 16^1 = 16

Therefore

16^5/4 * 16^1/4 / (16^1/2) ^2

= 16^ (5/16) / 16

=16^ (5/6) * 16^-1

= 16^ (5/6) - 1

= 16^-1/6)

, The simplified expression is 16^-1/6