Question

approximate the number using a calculator.
$8^{1.7}$

$8^{1.7} \approx \boxed{22.914}$ (round to three decimal places.)

Explanation:

Step1: Rewrite exponent for clarity

$8^{1.7} = 8^{\frac{17}{10}} = \sqrt[10]{8^{17}}$

Step2: Calculate with calculator

First compute $8^{17}=2251799813685248$, then take 10th root, or directly input $8^{1.7}$ into calculator:
$8^{1.7} \approx 22.94427191$

Step3: Round to 3 decimal places

Look at 4th decimal (2), which is <5, so truncate after 3rd decimal.

Answer:

$8^{1.7} \approx 22.944$