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44^{44}

= 2^{88} x 11^{44}

Immediately, this has to be divded by 8^{n}, which is same as 2^{3n}

So, = \frac{2^{88} \times 11^{44}}{2^{3n}}

Thus, 2^{88-3n} should be greater than 0.

Now, the only way it is greater is for 88 - 3n be greater than 0. For n = 29 its at its max greater than 0.

**Video solution:**

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