How Are They All Linked Together?

Algebra Level 2

4a=55b=66c=77d=8\large \begin{aligned} {4^{\color{#D61F06}a}=5} \\ {5^{\color{#3D99F6}b}=6} \\ {6^{\color{#20A900}c}=7} \\ {7^{\color{magenta}d} = 8} \\ \end{aligned}

Supose a\color{#D61F06}{a}, b\color{#3D99F6}{b}, c \color{#20A900}{c} and d\color{magenta}{d} satisfy the system of equations above, find a×b×c×d\color{#D61F06}{a}\times \color{#3D99F6}{b}\times \color{#20A900}{c}\times \color{magenta}{d}.

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