üslü denklemler

Question

$\left( 0,125\right) ^{\dfrac {a+2} {5}}=16^{a-1}$ ise a kaçtır ?

Answer 1

$\begin{align*} & 0,125=\dfrac {1} {8}=2^{-3},16=\left( 2\right) ^{4}\\ & 2^{\dfrac {-3a-6} {5}}=2^{4a-4}\\ & \dfrac {-3a-6} {5}=4a-4\\ & 23a-20=-6\\ & 23a=14\\ & a=14 / 23\end{align*}$