a) \(4^3\cdot8^2\)
\(=\left(2^2\right)^3\cdot\left(2^3\right)^2\)
\(=2^6\cdot2^6\)
\(=2^{12}\)
b) \(9^6:27^2\)
\(=\left(3^2\right)^6:\left(3^3\right)^2\)
\(=3^{12}:3^6\)
\(=3^6\)
c) \(5^2\cdot7^4\cdot\left(\dfrac{25}{49}\right)^2\)
\(=5^2\cdot7^4\cdot\left(\dfrac{5}{7}^2\right)^2\)
\(=5^2\cdot7^4\cdot\left(\dfrac{5}{7}\right)^4\)
\(=5^2\cdot\left(\dfrac{7\cdot5}{7}\right)^4\)
\(=5^2\cdot5^4\)
\(=5^6\)
