\(\left(\dfrac{1}{2}\right)^3\cdot\left(\dfrac{1}{4}\right)^2\)
\(=\left(\dfrac{1}{2}\right)^3\cdot\left[\left(\dfrac{1}{2}\right)^2\right]^2\)
\(=\left(\dfrac{1}{2}\right)^3\cdot\left(\dfrac{1}{2}\right)^{2\cdot2}\)
\(=\left(\dfrac{1}{2}\right)^3\cdot\left(\dfrac{1}{2}\right)^4\)
\(=\left(\dfrac{1}{2}\right)^{3+4}\)
\(=\left(\dfrac{1}{2}\right)^7\)