9514 1404 393
Answer:
9/25
Step-by-step explanation:
The applicable rules of exponents are ...
(a/b)^c = (a^c)/(b^c)
(a^b)^c) = a^(bc)
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The given power of the fraction is ...
[tex]\left(\dfrac{27}{125}\right)^{\frac{2}{3}}=\dfrac{(3^3)^{\frac{2}{3}}}{(5^3)^\frac{2}{3}}=\dfrac{3^{(3\cdot\frac{2}{3})}}{5^{(3\cdot\frac{2}{3})}}=\dfrac{3^2}{5^2}=\boxed{\dfrac{9}{25}}[/tex]
