Question 4 Evaluate the expression to four decimal places, using a calculator. $$ 4^{2.8}= $$ Question Help: Fin Video R eBook

Question

UpStudy AI · Accepted Answer

1. Rewrite the expression in a more convenient form by noting that
   $$
   4^{2.8} = \left(2^2\right)^{2.8} = 2^{2 \times 2.8} = 2^{5.6}.
   $$

2. Express $$2^{5.6}$$ using the exponential function:
   $$
   2^{5.6} = e^{5.6 \ln 2}.
   $$

3. Calculate the exponent:
   $$
   5.6 \ln 2 \approx 5.6 \times 0.6931471806 \approx 3.8816242112.
   $$

4. Evaluate the exponential:
   $$
   e^{3.8816242112} \approx 48.5125.
   $$

Thus, to four decimal places,
$$
4^{2.8} \approx 48.5125.
$$
$$4^{2.8} \approx 48.5125$$

Question 4 Evaluate the expression to four decimal places, using a calculator. \( 4^{2.8}= \) Question Help: Fin Video R eBook