By what number should `(-20)^(-1)` be divided to obtain `(-10)^(-1)` ?

Answer

To solve the problem of finding the number by which \((-20)^{-1}\) should be divided to obtain \((-10)^{-1}\), we can follow these steps:

### Step 1: Set up the equation
Let \( x \) be the number we need to find. According to the problem, we have:
\[ \frac{(-20)^{-1}}{x} = (-10)^{-1} \]

### Step 2: Rearrange the equation
To isolate \( x \), we can multiply both sides of the equation by \( x \) and then multiply both sides by \((-10)\):
\[ (-20)^{-1} = (-10)^{-1} \cdot x \]

### Step 3: Solve for \( x \)
Now, we can express \( x \) in terms of \((-20)^{-1}\) and \((-10)^{-1}\):
\[ x = \frac{(-20)^{-1}}{(-10)^{-1}} \]

### Step 4: Simplify the expression
Using the property of exponents that states \(\frac{a^{-1}}{b^{-1}} = \frac{b}{a}\), we can simplify:
\[ x = \frac{(-10)}{(-20)} \]

### Step 5: Simplify further
Now, we can simplify \(\frac{-10}{-20}\):
\[ x = \frac{10}{20} = \frac{1}{2} \]

### Step 6: Final answer
Thus, the number by which \((-20)^{-1}\) should be divided to obtain \((-10)^{-1}\) is:
\[ \boxed{\frac{1}{2}} \]

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