Question

please answer correctly with all the steps....​

Answer 1

Let the unknown number be x.

According to the question,

${( - 12)}^{ - 1} \div x = {( \frac{2}{3} )}^{ - 1} \\ \\ \implies \frac{ - 1}{12} \div x = \frac{3}{2} \\ \\ \implies \frac{ - 1}{12} = \frac{3}{2x} \\ \\ \implies \frac{ - 1}{6} = \frac{3}{x} \\ \\ \implies \boxed{ x = - 18}$

so, it should be noted that

(a/b)^ -c =(b/a)^c