Simplify. \[ \left(\frac{2 m^{3}}{3 m^{7}}\right)^{-3} \] Write your answer using only positive exponents.

To simplify the expression \(\left(\frac{2 m^{3}}{3 m^{7}}\right)^{-3}\), we first handle the negative exponent by taking the reciprocal: \[ \left(\frac{2 m^{3}}{3 m^{7}}\right)^{-3} = \left(\frac{3 m^{7}}{2 m^{3}}\right)^{3} \] Now, apply the exponent to both the numerator and the denominator: \[ = \frac{(3 m^{7})^{3}}{(2 m^{3})^{3}} \] Calculating the numerator and denominator separately: Numerator: \[ (3 m^{7})^{3} = 3^{3} (m^{7})^{3} = 27 m^{21} \] Denominator: \[ (2 m^{3})^{3} = 2^{3} (m^{3})^{3} = 8 m^{9} \] Putting it all together, we get: \[ = \frac{27 m^{21}}{8 m^{9}} \] Next, we simplify the fraction by using the property of exponents \(m^{a}/m^{b} = m^{a-b}\): \[ = \frac{27}{8} m^{21-9} = \frac{27}{8} m^{12} \] Thus, the simplified expression is: \[ \frac{27 m^{12}}{8} \] This final result contains only positive exponents.