Question

By what no. should 3 to the power -2 be divided to get 9 to the power -3.
Please solve this question quickly and with every step.

Answer 1

Let x be the required number. 

Now, solve the given equation to get the required number. 
$\frac{3^{-2} }{x} = 9^{-3}$
$\frac{ \frac{1}{9} }{ \frac{x}{1} } = \frac{1}{9^{3} }$
$\frac{1}{9x} = \frac{1}{729}$
Now, I am going to use cross multiplication. 
I am using * for multiplication. 
$729 * 1 = 9x * 1$
$9x = 729$
$\frac{9x}{9} = \frac{729}{9}$
$x = 81$

∴ The required number is 81 (=3²). 

Hope this may help you.