# How Are They All Linked Together?

Algebra Level 2

$\large \begin{eqnarray} {4^{\color{red}a}=5} \\ {5^{\color{blue}b}=6} \\ {6^{\color{green}c}=7} \\ {7^{\color{magenta}d} = 8} \\ \end{eqnarray}$

Supose $$\color{red}{a}$$, $$\color{blue}{b}$$, $$\color{green}{c}$$ and $$\color{magenta}{d}$$ satisfy the system of equations above, find $$\color{red}{a}\times \color{blue}{b}\times \color{green}{c}\times \color{magenta}{d}$$.

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