a) \(\left(\dfrac{1}{5}\right)^5\cdot5^5\)
\(=\left(\dfrac{1}{5}\cdot5\right)^5\)
\(=\left(\dfrac{5}{5}\right)^5\)
\(=1^5\)
\(=1\)
b) \(\left(\dfrac{2}{5}\right)^9\cdot5^9\)
\(=\left(\dfrac{2}{5}\cdot5\right)^9\)
\(=\left(\dfrac{10}{5}\right)^9\)
\(=2^9\)
\(=512\)
c) \(\left(\dfrac{4}{9}\right)^3\cdot3^3\)
\(=\left(\dfrac{4}{9}\cdot3\right)^3\)
\(=\left(\dfrac{12}{9}\right)^3\)
\(=\left(\dfrac{4}{3}\right)^3\)
\(=\dfrac{64}{27}\)