Question 103

If b is the largest natural number that divides $$8^{8}$$ and $$b = a^{3}$$ for some $$a \epsilon N$$, then what s the value of a?

Solution

Since we know that b is a cube, we should try to express b in terms of its prime factors to get a clear idea on how to proceed.
$$b=8^8=\left(2^3\right)^8=2^{3\times\ 8}=2^{24}$$
Now, $$b=a^3=2^{24}$$
$$a=\sqrt[\ 3]{2^{24}}=2^{\frac{24}{3}}=2^8$$
Which is equal to 256

Therefore, Option A is the correct answer.

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