Multiplication with same base: $ a^m * a^n = a^{m+n} $ Multiplication with different base but same powers: $ a^m * b^m = (a*b)^m $ Multiplication with different bases and different powers: $ a^m*b^n = (a^m)*(b^n) $ When the exponent is a logarithm: $ \exp\big\{\ln(a^b) \big\}=a^b $