$\frac{2^{288}}{2^{n}} = 512$ . What Is the Value of $n$ ?

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Solution

Finding the value of $n$ :
Given:
$\frac{2^{288}}{2^{n}} = 512$
$512$ can be written as $2^{9}$
Thus, the given equation becomes:
$\frac{2^{288}}{2^{n}} = 2^{9}$
we have a formula , $\frac{a^{m}}{a^{n}} = a^{m - n}$ so
$2^{288 - n} = 2^{9}$
As the base values are equal, we can equate the powers.
$288 - n = 9$
$\Rightarrow$ $n = 288 - 9$
$\Rightarrow$ $n = 279$
Therefore, the value of $n$ is $279$ .
Hence, the answer for given question is $279$ .

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