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If $6370=2^m.5^n.7^k.13^p$, then find $m+n+k+p$.
Given :
The given expression is $6370 = 2^m . 5^n . 7^k . 13^p$.
To do :
We have to find the value of $m + n + k + p$.
Solution :
Factorisation of 6370 is,
2 | 6370
__|______
5 | 3185
__|______
7 | 637
__|______
7 | 91
__|______
13
$6370 = 2 \times 5 \times 7 \times 7 \times 13$
$= 2 \times 5 \times 7^2 \times 13$
It is given that, $6370 = 2^m . 5^n . 7^k . 13^p$
On comparing,
$ 2^m . 5^n . 7^k . 13^p = 2 \times 5 \times 7^2 \times 13$
$m = 1$
$n = 1$
$k = 2$
$p = 1$
$m + n + k + p = 1 + 1 + 2 + 1$
$m + n + k + p = 5$.
Therefore, the value of $m + n + k + p$ is 5
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