Evaluate: номер

Expression: ${4}^{2x} \leq 0.25$

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

${2}^{4x} \leq 0.25$

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

${2}^{4x} \leq {2}^{-2}$

Since the bases are equal and greater than $1$, compare the exponents

$4x \leq -2$

Divide both sides of the inequality by $4$

$\begin{align*}&x \leq -\frac{ 1 }{ 2 } \\&\begin{array} { l }\begin{array} { l }\begin{array} { l }x \leq -0.5,& x \leq -{2}^{-1}\end{array},& x \in \left\langle-\infty, -\frac{ 1 }{ 2 }\right]\end{array}\end{array}\end{align*}$