Fill in the blanks:
(i) `(-23)/(17)xx (18)/(35)= (18)/(35) xx (.......) `
(ii) `-38xx(-7)/(19)=(-7)/(19)xx (.....)`
(iii) `((15)/(7)xx (-21)/(10)) xx (-5)/(6) = (........) xx ((-21)/(10) xx (-5)/(6))`
(iv) `(-12)/(5) xx ((4)/(15)xx (25)/(-16))=((-12)/(5)xx (4)/(15))xx(........)`

Answer

Let's solve the question step by step.

### Part (i)
We need to fill in the blank for the equation:
\[ \frac{-23}{17} \times \frac{18}{35} = \frac{18}{35} \times (.......) \]

1. **Rearranging the equation**: We can use the property of multiplication which states that if \( a \times b = b \times c \), then \( a = c \). Here, we can see that \( \frac{18}{35} \) is common on both sides.

2. **Identifying the missing term**: Thus, we can write:
\[ \frac{-23}{17} = (.......) \]

So, the answer is:
\[ \frac{-23}{17} \]

### Part (ii)
We need to fill in the blank for the equation:
\[ -38 \times \frac{-7}{19} = \frac{-7}{19} \times (.....) \]

1. **Rearranging the equation**: Again, using the property of multiplication:
\[ -38 = (.....) \]

2. **Identifying the missing term**: Therefore, the missing term is:
\[ -38 \]

### Part (iii)
We need to fill in the blank for the equation:
\[ \left(\frac{15}{7} \times \frac{-21}{10}\right) \times \frac{-5}{6} = (........) \times \left(\frac{-21}{10} \times \frac{-5}{6}\right) \]

1. **Rearranging the equation**: We can use the same property of multiplication:
\[ \left(\frac{15}{7}\right) \times \frac{-5}{6} = (........) \]

2. **Identifying the missing term**: Thus, the missing term is:
\[ \frac{15}{7} \]

### Part (iv)
We need to fill in the blank for the equation:
\[ \frac{-12}{5} \times \left(\frac{4}{15} \times \frac{25}{-16}\right) = \left(\frac{-12}{5} \times \frac{4}{15}\right) \times (........) \]

1. **Rearranging the equation**: Using the property of multiplication:
\[ \left(\frac{25}{-16}\right) = (........) \]

2. **Identifying the missing term**: Therefore, the missing term is:
\[ \frac{25}{-16} \]

### Final Answers
(i) \(\frac{-23}{17}\)
(ii) \(-38\)
(iii) \(\frac{15}{7}\)
(iv) \(\frac{25}{-16}\)