Question

By what number should $\left(-30\right)^{-1}$ be divided to get $6^{-1}$?

Answer 1

Hint: We are given that $\left(-30\right)^{-1}$ when divided by a number gives $6^{-1}$ and we are required to find that number. So, we first have to assume that the number is equal to some variable $x$. After that we will use the information given to create a linear equation in one variable. After that we will solve for that variable $x$ and hence the answer will be found out.

Complete step by step solution:
We are required to find the number that should be divided by $\left(-30\right)^{-1}$ to get $6^{-1}$. We assume that the number is $x$. Then according to the given information:
$\dfrac{\left(-30\right)^{-1}}{x}=6^{-1}$
Now we will use the fact that for any real number $a$ other than 0:
$a^{-1}=\dfrac{1}{a}$
Using this in the equation we have created and also multiplying both the sides by $x$, we can say that:
$\dfrac{1}{-30}=\dfrac{1}{6}\times x$
Now multiplying both sides by 6 we get:
$\Rightarrow x=\dfrac{6}{-30}$
$\Rightarrow x=-\dfrac{1}{5}$
Now, if we want to convert it again in the form of power then:
$\Rightarrow x=\left(-5\right)^{-1}$
Hence, the number that should be divided by $\left(-30\right)^{-1}$ to get $6^{-1}$ is $\left(-5\right)^{-1}$. So, the answer has been found out.

Note: In questions like these, if you are unable to properly convert the power into fraction then it would lead to an invalid solution. So, make sure that you make the least calculation mistakes. You can directly answer this question by directly dividing $\dfrac{1}{-30}$ by $\dfrac{1}{6}$ if you are sure of your calculations. But assuming a variable and then doing that would produce more accurate results.