Step-by-step explanation:
Given;
We are given the exponential equation shown below;

Required;
We are required to
(i) Find a common base
(ii) Solve for x
Step by step solution;
To solve this problem we shall start with the following steps;
![[((5)/(2))^3]^(4x-1)=[((2)/(5))^4]^(x+1)](https://img.qammunity.org/2023/formulas/mathematics/college/nex43li8e2im3xxf78bz2cm28xenuedeln.png)
For the left side of the equation, we can refine by applying the rule of exponents;

Therefore, we now have;
![[((2)/(5))^(-3)]^(4x-1)=[((2)/(5))^4]^(x+1)](https://img.qammunity.org/2023/formulas/mathematics/college/e89rbs53e6s4shb76j5gw09e9tnkr4gdgi.png)

We now have a common base and that means;

Therefore;



Divide both sides by -16;

ANSWER:
