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The value of \(\frac{{{{\left( {243} \right)}^{0.13}} \times {{\left( {243} \right)}^{0.07}}}}{{{{\left( 7 \right)}^{0.25}} \times {{\left( {49} \right)}^{0.075}} \times {{\left( {343} \right)}^{0.2}}}}\) is
1. \(\frac{3}{7}\)
2. \(\frac{7}{3}\)
3. 1\(\frac{3}{7}\)
4. 2\(\frac{2}{7}\)

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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

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