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

Question

UpStudy AI · Accepted Answer

To determine the number $$ x $$ that you need to multiply by $$ (-6)^{-1} $$ to get $$ g^{-1} $$, you can set up the equation as follows:

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

Let's solve for $$ x $$:

1. **Express $$ (-6)^{-1} $$ as a fraction:**
   
   $$
   (-6)^{-1} = \frac{1}{-6} = -\frac{1}{6}
   $$

2. **Substitute into the equation:**

$$
   x \times \left(-\frac{1}{6}\right) = \frac{1}{g}
   $$

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

$$
   x = \frac{\frac{1}{g}}{-\frac{1}{6}} = \frac{1}{g} \times \left(-6\right) = -\frac{6}{g}
   $$

So, the number you need to multiply by $$ (-6)^{-1} $$ to obtain $$ g^{-1} $$ is:

$$
x = -\frac{6}{g}
$$

**Final Answer:**  
After simplifying, the required number is –6 divided by g. Thus,

x = −6 ⁄ g
The number to multiply $$ (-6)^{-1} $$ by to get $$ g^{-1} $$ is $$ -\frac{6}{g} $$.

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