Question

error analysis describe and correct the error in evaluating the expression. \\(\

$$\begin{align*}27^{2/3}&=(27^{1/3})^2\\\\&=9^2\\\\&=81\\end{align*}$$

\\) \\(\bigcirc\\) the exponent of 2/3 cannot be separated. \\(\bigcirc\\) the exponent of 1/3 should have been squared. \\(\bigcirc\\) the index and exponent were switched. \\(\bigcirc\\) the cube root of 27 was calculated incorrectly. \\(27^{2/3}=\square\\)

Explanation:

Step1: Identify the error

The cube root of 27 was miscalculated: $27^{1/3}
eq 9$, since $3^3=27$, so $27^{1/3}=3$.

Step2: Correct the calculation

First compute $27^{1/3}=3$, then square the result: $3^2=9$.
Alternatively, use the rule $a^{m/n}=\sqrt[n]{a^m}$: $\sqrt[3]{27^2}=\sqrt[3]{729}=9$.

Answer:

The correct error description is:
D. The cube root of 27 was calculated incorrectly.

$27^{2/3} = 9$