$\frac{16^{\frac{5}{4}}cdot16^{\frac{1}{4}}}{(16^{\frac{1}{2}})^2}=$

Explanation:

Step1: Use exponent - product rule

According to the rule (a^m\cdot a^n=a^{m + n}), for (16^{\frac{5}{4}}\cdot16^{\frac{1}{4}}), we have (16^{\frac{5}{4}+\frac{1}{4}}=16^{\frac{5 + 1}{4}}=16^{\frac{6}{4}}=16^{\frac{3}{2}}).

Step2: Use exponent - power rule

According to the rule ((a^m)^n=a^{mn}), for ((16^{\frac{1}{2}})^2), we have (16^{\frac{1}{2}\times2}=16^1 = 16).

Step3: Simplify the fraction

We now have (\frac{16^{\frac{3}{2}}}{16}). Since (16 = 16^1), and using the rule (\frac{a^m}{a^n}=a^{m - n}), we get (16^{\frac{3}{2}-1}=16^{\frac{3 - 2}{2}}=16^{\frac{1}{2}}). Since (16^{\frac{1}{2}}=\sqrt{16}=4).

Answer:

4