Answer
\[
\int_{1}^{27} x^{-\frac{2}{3}} d x=6
\]
Work Step by Step
The area below the curve $f(x)=x^{-\frac{2}{3}}$ over the interval [1,27] is $\int_{1}^{27} x^{-\frac{2}{3}} d x$
\[
\begin{aligned}
\int_{1}^{27} x^{-\frac{2}{3}} d x &=\left.2 \sqrt[3]{x}\right|_{1} ^{27} \\
&=[-\sqrt[3]{1}+\sqrt[3]{27}].3 \\
&=[-1+3].3 \\
&=\left[\begin{array}{ll}
6
\end{array}\right]
\end{aligned}
\]