Calculate: cube root of 2^{2x+5}}=0.25^{-2x

Expression: $\sqrt[3]{{2}^{2x+5}}={0.25}^{-2x}$

Write the expression in exponential form with the base of $2$

${2}^{\frac{ 2x+5 }{ 3 }}={0.25}^{-2x}$

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 $-10$

$\begin{align*}&x=\frac{ 1 }{ 2 } \\&\begin{array} { l }x=0.5,& x={2}^{-1}\end{array}\end{align*}$