1. **State the problem:** Simplify the expression $$2x^{8}y^{15} - \frac{40x^{10}y^{24}}{5x^{2}y^{9}}$$. 2. **Recall the rules:** - When dividing powers with the same base, subtract the exponents: $$\frac{a^{m}}{a^{n}} = a^{m-n}$$. - When multiplying or dividing coefficients, perform normal arithmetic. 3. **Simplify the fraction:** $$\frac{40x^{10}y^{24}}{5x^{2}y^{9}} = \frac{\cancel{40}^8 x^{10} y^{24}}{\cancel{5}^1 x^{2} y^{9}} = 8 x^{10-2} y^{24-9} = 8 x^{8} y^{15}$$ 4. **Rewrite the expression:** $$2x^{8}y^{15} - 8x^{8}y^{15}$$ 5. **Combine like terms:** $$ (2 - 8) x^{8} y^{15} = -6 x^{8} y^{15}$$ 6. **Final answer:** $$\boxed{-6 x^{8} y^{15}}$$