simplify.\n16^{\frac{3}{4}}

Explanation:

Step1: Rewrite 16 as a power - of 2

$16 = 2^4$, so $16^{\frac{3}{4}}=(2^4)^{\frac{3}{4}}$.

Step2: Apply the power - of - a - power rule

According to the rule $(a^m)^n=a^{mn}$, we have $(2^4)^{\frac{3}{4}} = 2^{4\times\frac{3}{4}}$.

Step3: Calculate the exponent

$4\times\frac{3}{4}=3$, so $2^{4\times\frac{3}{4}}=2^3$.

Step4: Evaluate $2^3$

$2^3 = 2\times2\times2=8$.

Answer:

8