If 35ab=345673 where a and b are both positive integers, then how many different

Question

35^{a} b = 3^{4} 5^{6} 7^{3}

where a and b are both positive integers, then how many different values can b take?

Options:

A . 1

B . 2

C . 3

D . >3

Answer: Option C
:
C

3^{4} 5^{6} 7^{3} = 3^{4} 35^{3} 5^{3}

The question states that the given expression will be written as

35^{a} b

where a and b are both positive integers, i.e. a can take values 1,2 or 3. For each of these values, b will have three different values. Hence answer is option (c).

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