Question

If $25025=p_1^{x_1}.p_2^{x_2}.p_3^{x_3}.p_4^{x_4}$ find the value of $p_1,p_2,p_3,p_4$ and $x_1,x_2,x_3,x_4$.

Answer 1

Given that,

$25025=p_1^{x_1}\times p_2^{x_2}\times p_3^{x_3}\times p_4^{x_4}$

To find out,

The values of $p_1,p_2,p_3,p_4,x_1,x_2,x_3$ and $x_4$

$25025$ can be represented as the product of its prime factors as:

$25025=5\times 5\times 7\times 11\times 13$

$\Rightarrow 25025=5^2\times 7^1\times {11}^1\times {13}^1...............\left(1\right)$

It is given that, $25025=p_1^{x_1}\times p_2^{x_2}\times p_3^{x_3}\times p_4^{x_4}...............\left(2\right)$

Comparing $\left(1\right)$ and $\left(2\right)$, we get,

$p_1=5,p_2=7,p_3=11,p_4=13,x_1=2,x_2=1,x_3=1$ and $x_4=1$

Hence, $p_1=5,p_2=7,p_3=11,p_4=13,x_1=2,x_2=1,x_3=1$ and $x_4=1$.