\(\left(\dfrac{1}{5}\right)^{25}\cdot\left(\dfrac{1}{5}\right)^{30}\)
\(=\left(\dfrac{1}{5}\right)^{25+30}\)
\(=\left(\dfrac{1}{5}\right)^{55}\)
\(\left(\dfrac{1}{16}\right)^3:\left(\dfrac{1}{8}\right)^2\)
\(=\left[\left(\dfrac{1}{2}\right)^4\right]^3:\left[\left(\dfrac{1}{2}\right)^3\right]^2\)
\(=\left(\dfrac{1}{2}\right)^{12}:\left(\dfrac{1}{2}\right)^6\)
\(=\left(\dfrac{1}{2}\right)^{12-6}=\left(\dfrac{1}{2}\right)^6\)
\(\left(x^3\right)^2:\left(x^2\right)^3\)
\(=x^{3\cdot2-2\cdot3}\)
\(=x^0=1\)