1. **State the problem:** We need to calculate the value of the expression $$-15 \times 2^{\frac{4}{5}}$$ and express the answer in its simplest form. 2. **Recall the rules:** The expression involves a negative coefficient multiplied by an exponential term with a fractional exponent. The fractional exponent $\frac{4}{5}$ means the fifth root of 2 raised to the 4th power, i.e., $$2^{\frac{4}{5}} = \left(\sqrt[5]{2}\right)^4$$. 3. **Calculate the exponential part:** $$2^{\frac{4}{5}} = \left(2^{\frac{1}{5}}\right)^4 = \left(\sqrt[5]{2}\right)^4$$ 4. **Multiply by -15:** $$-15 \times 2^{\frac{4}{5}} = -15 \times \left(\sqrt[5]{2}\right)^4$$ 5. **Final answer:** The simplest exact form is $$\boxed{-15 \times 2^{\frac{4}{5}}}$$ or equivalently $$\boxed{-15 \left(\sqrt[5]{2}\right)^4}$$. If a decimal approximation is needed, $2^{\frac{4}{5}} \approx 1.741$, so the value is approximately $$-15 \times 1.741 = -26.115$$. This completes the solution.