Simplify these expressions. Input @ for \( { }^{2} \) and \# for \( { }^{3} \). \[ v \times 7 x= \] \( \square \) [1] \( 2 m \times \) \( \square \) \( =18 m n \) [1] \( 9 c \times 6 e= \) \( \square \) [1] \( 5 x \times \) \( \square \) \( =30 x^{2} \) \( 8 a \times 5 a= \) \( \square \) [1] \( 4 w \times \) \( \square \) \( =16 w^{2} x \) \[ 5 x w \times 2 w= \] \( \square \) [1] \( 5 c \times \) \( \square \) \( =30 a c^{3} \) [2] \[ 7 m n \times 7 m^{2} n= \] \( \square \) [1] \( \square \) \( \times 3 w^{2} x=15 w^{3} x^{3} \) \[ 4 a c x \times 5 a x^{2} \times 6 c= \] \( \square \) [2] \( \square \) \[ \times 4 a c^{2} e^{3}=20 a^{3} c^{3} e^{3} \] Mark it

Sure! Let's simplify each expression step-by-step: 1. \( v \times 7 x = 7 vx \) 2. \( 2 m \times \square = 18 m n \) Therefore, \( \square = 9 n \) (since \( 2m \times 9n = 18mn \)). 3. \( 9 c \times 6 e = 54 ce \) 4. \( 5 x \times \square = 30 x^{2} \) Thus, \( \square = 6 x \) (as \( 5x \times 6x = 30x^{2} \)). 5. \( 8 a \times 5 a = 40 a^{2} \) 6. \( 4 w \times \square = 16 w^{2} x \) Hence, \( \square = 4 wx \). 7. \( 5 x w \times 2 w = 10 x w^{2} \) 8. \( 5 c \times \square = 30 a c^{3} \) So, \( \square = 6 a c^{2} \). 9. \( 7 m n \times 7 m^{2} n = 49 m^{3} n^{2} \) 10. \( \square \times 3 w^{2} x = 15 w^{3} x^{3} \) This gives \( \square = 5 w x^{2}\). 11. \( 4 a c x \times 5 a x^{2} \times 6 c = 120 a^{2} c^{2} x^{3} \) 12. The final expression with \( 4 a c^{2} e^{3} = 20 a^{3} c^{3} e^{3} \). If you're ready to tackle even more of these or need some tips on common mistakes in simplifying, just let me know!