If 49392=a4b2c3, find the values of a, b and c,


If $49392=a^{4} b^{2} a^{2} c^{3}$, find the values of $a, b$ and $c$, where $a, b$ and $c$ are different positive primes.


First find out the prime factorisation of 49392.

It can be observed that 49392 can be written as $2^{4} \times 3^{2} \times 7^{3}$, where 2,3 and 7 are positive primes.

$\therefore 49392=2^{4} 3^{2} 7^{3}=a^{4} b^{2} c^{3}$

$\Rightarrow a=2, b=3, c=7$

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