Answer:
1/9
Step-by-step explanation:
[tex]27^{-\frac{2}{3}}[/tex]
To simplify the expression with fractional exponent , we write the base 27 in exponential form
[tex]27= 3 \cdot 3 \cdot 3= 3^3[/tex]
[tex](3^3)^{-\frac{2}{3}}[/tex]
Now we apply exponential property
[tex](a^m)^n= a^{mn}[/tex]
[tex]3^{3 \cdot {-\frac{2}{3}}[/tex]
[tex]3^{-2}[/tex]
Write the answer with positive exponent, move the exponent to the denominator.
[tex]\frac{1}{3^2} =\frac{1}{9}[/tex]
