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Here, It is said that abc = 125 If we factorise 125 then we will find that the possible factors are 5, 5 and again 5. It's because
\( 5^{3}\) = 125
So, a = b = c = 5
Now, it is given that \( a^{x}\) = \( b^{y}\) = \( c^{z}\) = \( 5^{11}\)
We know that a = b = c = 5. So, the only possible value for x, y, z is 11.
Hence, x = y = z = 11
Finally , our work is to simplify the expression and it would be easy as all the values are known.
\( \frac{xy + yz + zx}{ xyz }\)
= \( \frac{11 * 11 + 11* 11 + 11* 11}{ 11 * 11* 11 }\)
= \( \frac{121 + 121 + 121}{ 1331 }\)
= \( \frac{ 363 }{ 1331 }\)
= \( \frac{ 3 }{ 11 }\)
Hence, Final answer is = \( \frac{ 3 }{ 11 }\)