Question

approximate the number using a calculator. $2^{2.2}$
$2^{2.2} \approx \square$ (round to three decimal places.)

Explanation:

Step1: Rewrite exponent as fraction

$2^{2.2} = 2^{\frac{11}{5}}$

Step2: Rewrite as root form

$2^{\frac{11}{5}} = \sqrt[5]{2^{11}}$

Step3: Calculate $2^{11}$

$2^{11}=2048$

Step4: Compute 5th root of 2048

$\sqrt[5]{2048} \approx 4.594793419$

Step5: Round to 3 decimal places

Look at 4th decimal digit (7), round up the 3rd digit (4) to 5.

Answer:

$4.595$