Question

approximate the number using a calculator.
$4^{2.6}$
$4^{2.6} \approx \square$ (round to three decimal places.)

Explanation:

Step1: Rewrite exponent as fraction

$2.6 = \frac{13}{5}$, so $4^{2.6} = 4^{\frac{13}{5}}$

Step2: Rewrite as root and power

$4^{\frac{13}{5}} = \sqrt[5]{4^{13}}$

Step3: Calculate $4^{13}$ first

$4^{13} = 67108864$

Step4: Compute 5th root and round

Calculate $\sqrt[5]{67108864} \approx 24.9807$
Round to 3 decimal places: $24.981$

Answer:

$24.981$