For the positive integers a and b, k' represents the number of zeros between the decimal point and the first nonzero digit to the right of the decimal point in the reciprocal of the product of a and b, when that reciprocal is expressed as a terminating decimal. What is the value of k' (6^5, 5^6) ?

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Official Explanation

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The function defined works like this:

k'(2,5) = \frac{1}{2} \times \frac{1}{5} = \frac{1}{10}

= 0 (Number of zeros between the decimal point and the first nonzero digit to the right of the decimal point)

So,

k'(6^5, 5^6) = \frac{1}{6^{5}} \times \frac{1}{5^{6}} = \frac{1}{2^{5} \times 3^{5} \times 5^{5} \times 5}

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What this question tests

Your ability to evaluate and compose functions, including unusual defined operations.

Applying function operations in the wrong order or ignoring domain restrictions.