Evaluate: 27^{(-2)/(3)}=(1)/(9)

Expression: ${27}^{\frac{ -2 }{ 3 }}=\frac{ 1 }{ 9 }$

Take the logarithm of both sides of the equation

$\log_{ 27 }({ {27}^{\frac{ -2 }{ 3 }} })=\log_{ 27 }({ \frac{ 1 }{ 9 } })$

Use $\log_{ a }({ {a}^{x} })=x$ to simplify the expression

$-\frac{ 2 }{ 3 }=\log_{ 27 }({ \frac{ 1 }{ 9 } })$

Swap the sides of the equation

$\log_{ 27 }({ \frac{ 1 }{ 9 } })=-\frac{ 2 }{ 3 }$