Correct Answer - Option 1 :
\(\frac{3}{7}\)
Concept used:
am × an = a(m + n)
Calculation:
⇒ \(\frac{{{{\left( {243} \right)}^{0.13}} × {{\left( {243} \right)}^{0.07}}}}{{{{\left( 7 \right)}^{0.25}} × {{\left( {49} \right)}^{0.075}} × {{\left( {343} \right)}^{0.2}}}}\)
⇒ [(3)5 × 0.13 × (3)5 × 0.07]/[(7)0.25 × (7)2 × 0.075 × (7)3 × 0.2]
⇒ [(3)0.65 × (3)0.35]/[(7)0.25 × (7)0.15 × (7)0.6]
Using law of indices:
⇒ am × an = a(m + n)
⇒ ? = 31/71
∴ ? = 3/7