### Instruction: What is the value of $\displaystyle{(2^3)}^{\frac{4}{3}}$?### Response: I notice that the expression has a power raised to another power, which means I can use the rule $(a^b)^c = a^{bc}$ to simplify it.
Applying this rule, I get $\displaystyle{(2^3)}^{\frac{4}{3}} = 2^{3 \cdot \frac{4}{3}}$.
Multiplying the exponents, I get $2^{3 \cdot \frac{4}{3}} = 2^4$.