Base and Powers

$2^{2x} \times 4^{8x} = 2^{2x} \times 2^{16x} =2^{18x}$

$8^{18} =2^{3*18}=2^{54}$

so , $18x=54$ , $x=3$

$\large \begin{aligned} 2^{2x} \cdot 4^{8x} & = 8^{18} \\ \Rightarrow 4^x \cdot 4^{8x} & = [(4^{\frac12})^3]^{18} \\ \Rightarrow 4^{9x} & = 4^{\frac{18 \times 3}2} \\ \Rightarrow 4^{9x} & = 4^{27} \\ \Rightarrow 9x & =27 \\ \implies x & = \boxed 3 \\ \end{aligned}$

$2^{2x} \times 4^{8x} = 8^{18}$

$2^{2x} \times 2^{2(8x)} = 2^{3(18)}$

$2x + 16x = 3(18)$

$\boxed{x = 3}$

$\begin{aligned} 2^{2x} \times 4^{8x} & = 8^{18} \\ 2^{2x} \times 2^{2\times 8x} & = 2^{3\times 18} \\ 2^{2x+16x} & = 2^{3\times 18} \\ \implies 18x & = 3\times 18 \\ x & = \boxed 3 \end{aligned}$

Make all bas get 2 and make a equation with quotient 2x+16x=54 18x=54 so x=3