${2}^{\frac{ 2x+5 }{ 3 }}={0.25}^{-2x}$
Write the expression in exponential form with the base of $2$${2}^{\frac{ 2x+5 }{ 3 }}={2}^{4x}$
Since the bases are the same, set the exponents equal$\frac{ 2x+5 }{ 3 }=4x$
Multiply both sides of the equation by $3$$2x+5=12x$
Move the constant to the right-hand side and change its sign$2x=12x-5$
Move the variable to the left-hand side and change its sign$2x-12x=-5$
Collect like terms$-10x=-5$
Divide both sides of the equation by $-10$$\begin{align*}&x=\frac{ 1 }{ 2 } \\&\begin{array} { l }x=0.5,& x={2}^{-1}\end{array}\end{align*}$