evaluate the expression using technology. round your answer to two decimal places, if necessary.\n$20,736^{4/…
evaluate the expression using technology. round your answer to two decimal places, if necessary.\n$20,736^{4/5} \\approx$
Answer
Explanation:
Step1: Rewrite exponent as root/power
Recall that $a^{m/n} = \left(\sqrt[n]{a}\right)^m$. So: $20736^{4/5} = \left(\sqrt[5]{20736}\right)^4$
Step2: Calculate 5th root of 20736
Using technology, $\sqrt[5]{20736} \approx 6.9883$
Step3: Raise result to the 4th power
$\left(6.9883\right)^4 \approx 6.9883 \times 6.9883 \times 6.9883 \times 6.9883 \approx 2220.65$
Answer:
$2220.65$