Question

20,736^{4/5} \approx \square

Explanation:

Step1: Rewrite root as exponent

Recall that $a^{1/n} = \sqrt[n]{a}$, so $20736^{1/5} = \sqrt[5]{20736}$

Step2: Use logarithm to simplify

Take natural log: $\ln(20736^{1/5}) = \frac{1}{5}\ln(20736)$
Calculate $\ln(20739) \approx 9.942$, so $\frac{1}{5} \times 9.942 = 1.9884$

Step3: Convert back to exponential

$e^{1.9884} \approx 7.3$
(Alternatively, test integer powers: $7^5=16807$, $8^5=32768$; 20736 is between them, use linear approximation: $\frac{20736-16807}{32768-16807} \approx 0.246$, so $7 + 0.246 \approx 7.25 \approx 7.3$)

Answer:

$7.3$