Evaluate $16^{7/4}$.
We have  \[16^{7/4} = (2^4)^{7/4} = 2^{4\cdot (7/4)} = 2^7 = \boxed{128}.\]
128
Level 1
Algebra
Problem: Evaluate $16^{7/4}$.
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To evaluate $16^{7/4}$, first recognize that $16$ can be expressed as a power of $2$: $16 = 2^4$. Substituting this into the expression gives $16^{7/4} = (2^4)^{7/4}$. 

Next, apply the power of a power property of exponents, which states that $(a^m)^n = a^{m \cdot n}$. Thus, $(2^4)^{7/4} = 2^{4 \cdot (7/4)}$. 

Calculating the exponent, $4 \cdot (7/4) = 7$. Therefore, we have $16^{7/4} = 2^7$. 

Now, compute $2^7$. This can be done by multiplying $2$ by itself seven times: $2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$. 

Calculating step-by-step: 
- $2 \times 2 = 4$
- $4 \times 2 = 8$
- $8 \times 2 = 16$
- $16 \times 2 = 32$
- $32 \times 2 = 64$
- $64 \times 2 = 128$

Thus, $2^7 = 128$. 

The final answer is $128$.<|END_OF_LATENT|> The final answer is $128$.