By what number should $$ (-6)^{-1} $$ be multiplid so that the product becomes $$ 9^{-1} $$

Question

UpStudy AI · Accepted Answer

To find the number $$ x $$ such that:

$$
(-6)^{-1} \times x = 9^{-1}
$$

Let's solve for $$ x $$:

1. **Understand the Negative Exponents:**

$$
   (-6)^{-1} = \frac{1}{-6} = -\frac{1}{6}
   $$
   
   $$
   9^{-1} = \frac{1}{9}
   $$

2. **Set Up the Equation:**

$$
   -\frac{1}{6} \times x = \frac{1}{9}
   $$

3. **Solve for $$ x $$:**

Multiply both sides by $$ -6 $$ to isolate $$ x $$:

$$
   x = \frac{1}{9} \times (-6) = -\frac{6}{9} = -\frac{2}{3}
   $$

**Therefore, the number $$ x $$ is $$-\frac{2}{3}$$.**
The number to multiply $$ (-6)^{-1} $$ by to get $$ 9^{-1} $$ is $$-\frac{2}{3}$$.

By what number should \( (-6)^{-1} \) be multiplid so that the product becomes \( 9^{-1} \)