Question

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

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Solution

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

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