simplify. 16^{\frac{7}{4}}

Explanation:

Step1: Rewrite 16 as a power - base.

$16 = 2^4$, so $16^{\frac{7}{4}}=(2^4)^{\frac{7}{4}}$

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

According to the rule $(a^m)^n=a^{mn}$, we have $(2^4)^{\frac{7}{4}}=2^{4\times\frac{7}{4}}$

Step3: Calculate the exponent.

$4\times\frac{7}{4}=7$, so $2^{4\times\frac{7}{4}} = 2^7$

Step4: Evaluate $2^7$.

$2^7=2\times2\times2\times2\times2\times2\times2 = 128$

Answer:

$128$