Simplify: \[ \left(\frac{2 a^{3}}{b^{6} c^{7}}\right)^{3} \]

Step 1 ：Given the expression \(\left(\frac{2 a^{3}}{b^{6} c^{7}}\right)^{3}\)

Step 2 ：We can simplify this by applying the power of a power rule, which states that \((a^m)^n = a^{m*n}\).

Step 3 ：Applying this rule to each term in the fraction, we get \(\frac{8 a^{9}}{b^{18} c^{21}}\)

Step 4 ：So, the simplified form of the given expression is \(\boxed{\frac{8 a^{9}}{b^{18} c^{21}}\)