Question

By what number should 3 power of - 4 be multiplied so that the product is 729

Answer 1

${3}^{10} \\ as \: {3}^{10} \times {3}^{ - 4} = {3}^{10 - 4 } \\ {3}^{6} = 729$

Answer 2

$\fontsize{18}{10}{\textup{\textbf{The number is 59029.}}}$

Step-by-step explanation:

We will be using the following property of indices :

$\dfrac{x^a}{x^b}=x^{a-b}.$

Let the required number be n.

Then, according to the given information, we must have

$3^{-4}\times n=729\\\\\Rightarrow 3^{-4}\times n=3^6\\\\\Rightarrow n=\dfrac{3^6}{3^{-4}}\\\\\Rightarrow n=3^{6-(-4)}\\\\\Rightarrow n=3^{10}\\\\\Rightarrow n=59049.$

Thus, the required number to be multiplied is 59049.

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