1. **State the problem:** Simplify the expression $$\frac{16x^{40}y^{18}x^{14}}{y^{18}w^{14}}^{19} = 16^4 x^A y^B w^C$$ and identify the integers $A$, $B$, $C$, and $D$. 2. **Rewrite the expression inside the parentheses:** Combine like terms in the numerator: $$16x^{40}x^{14}y^{18} = 16x^{54}y^{18}$$ So the expression inside the parentheses is: $$\frac{16x^{54}y^{18}}{y^{18}w^{14}}$$ 3. **Simplify inside the parentheses:** Cancel $y^{18}$ in numerator and denominator: $$\frac{16x^{54}}{w^{14}}$$ 4. **Apply the exponent 19 to each factor:** $$\left(\frac{16x^{54}}{w^{14}}\right)^{19} = \frac{16^{19} x^{54 \times 19}}{w^{14 \times 19}} = \frac{16^{19} x^{1026}}{w^{266}}$$ 5. **Express the right side as given:** $$16^4 x^A y^B w^C$$ Since there is no $y$ term on the left after simplification, $B=0$. 6. **Equate the powers of 16:** $$16^{19} = 16^4 \implies$$ This is not equal unless we rewrite the expression or interpret the problem differently. But the problem states the expression equals $$16^4 x^B y^C w^D$$, so likely the problem wants the expression simplified to that form with exponents $A$, $B$, $C$, $D$. 7. **Rewrite $16^{19}$ as $16^4 \times 16^{15}$:** $$16^{19} = 16^4 \times 16^{15}$$ So the expression is: $$16^4 \times 16^{15} x^{1026} w^{-266}$$ 8. **Match the expression to the form:** $$16^4 x^A y^B w^D$$ Therefore: - $A = 1026$ - $B = 0$ - $D = -266$ 9. **Since $y$ is canceled, $C$ is 0.** **Final answer:** $$A=1026, B=0, C=0, D=-266$$