We are given that the following ratios are equivalent:
[tex]\begin{gathered} x\colon8 \\ 27\colon x^2 \end{gathered}[/tex]
This means that the following relationship holds:
[tex]\frac{x}{8}=\frac{27}{x^2}[/tex]
Now, to solve for "x" we can cross multiply the equation:
[tex]x\times x^2=27\times8[/tex]
Solving the operations:
[tex]x^3=216[/tex]
Now we take the cubic root to both sides:
[tex]x=\sqrt[3]{216}[/tex]
Solving the operation:
[tex]x=6[/tex]
Therefore, the value of "x" is 6.
