Find the value of m which satisfies \(\left(\dfrac{22}{5}\right)^{18} \times \left(\dfrac{5}{22}\right)^{8} \times \left(\dfrac{22}{5}\right)^{6} = \left(\dfrac{5}{22}\right)^{9m+4}.\)
\(-\dfrac{20}{9}\)
Left side: \(\left(\dfrac{22}{5}\right)^{18}\times\left(\dfrac{5}{22}\right)^{8}\times\left(\dfrac{22}{5}\right)^{6} = \left(\dfrac{22}{5}\right)^{18+6}\times\left(\dfrac{22}{5}\right)^{-8} = \left(\dfrac{22}{5}\right)^{16}\).
Right side: \(\left(\dfrac{5}{22}\right)^{9m+4} = \left(\dfrac{22}{5}\right)^{-(9m+4)}\).
Equating exponents: \(16 = -(9m+4) \Rightarrow 9m+4 = -16 \Rightarrow 9m = -20 \Rightarrow m = -\dfrac{20}{9}\).
Hence, the value of m is \(-\tfrac{20}{9}\).
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