To approximate $4^{2.4}$ to three decimal places using a calculator:

1. Compute $4^{2.4}$:
   • This can be done by calculating $4^{2.4} = e^{2.4 \cdot \ln(4)}$ on most scientific calculators.
   • Alternatively, directly use the exponentiation feature of the calculator.

Result:

• $4^{2.4} \approx 27.856$ (rounded to three decimal places).

Would you like further clarification or steps to input this into your calculator?

Here are 5 related questions:

1. How do you compute other fractional exponents like $3^{1.7}$?
2. What is the difference between using $\ln(x)$ and $\log(x)$ in these calculations?
3. How can this approximation method help in solving equations involving exponents?
4. Can fractional exponents be rewritten as roots and powers, and how would you do it for $4^{2.4}$?
5. What is the real-life application of such exponential calculations?

Tip: Ensure your calculator is set to the correct mode (degrees or radians) when working with logarithms or trigonometric functions. For exponents, this setting is generally not relevant.