1. **State the problem:** Simplify the expression $$\left(\frac{j^{15}}{8}\right)^{\frac{2}{3}}$$ and find which of the given options is equivalent. 2. **Recall the exponent rule:** For any expression $$\left(\frac{a}{b}\right)^m = \frac{a^m}{b^m}$$ and for powers of powers $$\left(x^n\right)^m = x^{nm}$$. 3. **Apply the power to numerator and denominator:** $$\left(\frac{j^{15}}{8}\right)^{\frac{2}{3}} = \frac{\left(j^{15}\right)^{\frac{2}{3}}}{8^{\frac{2}{3}}}$$ 4. **Simplify numerator:** $$\left(j^{15}\right)^{\frac{2}{3}} = j^{15 \times \frac{2}{3}} = j^{10}$$ 5. **Simplify denominator:** $$8^{\frac{2}{3}} = \left(2^3\right)^{\frac{2}{3}} = 2^{3 \times \frac{2}{3}} = 2^2 = 4$$ 6. **Combine numerator and denominator:** $$\frac{j^{10}}{4}$$ 7. **Conclusion:** The expression simplifies to $$\frac{j^{10}}{4}$$ which corresponds to answer choice A. **Final answer:** $$\boxed{\frac{j^{10}}{4}}$$