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What will come in the place of the question mark ‘?’ in the following question?

\(\frac{{(243)}^{0.13} \times (243)^{0.07}}{ (7)^{0.25} \times (49)^{0.075} \times (343)^{0.2}} =?\)


1. \(\frac{3}{8}\)
2. \(\frac{3}{7}\)
3. \(\frac{7}{3}\)
4. \(\frac{4}{5}\)

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Best answer
Correct Answer - Option 2 : \(\frac{3}{7}\)

Concepts used:

(am)= a(m × n)

am × a = a(m + n) 

Calculation:

\(\frac{{(243)}^{0.13} \times (243)^{0.07}}{ (7)^{0.25} \times (49)^{0.075} \times (343)^{0.2}}\)

⇒ [{(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) ÷ (70.25 × 70.15 × 70.6)]

⇒ [3(0.65 + 0.35) ÷ 7(0.25 + 0.15 + 0.6)]

⇒ (31.0 ÷ 71.0)

⇒ 3/7

∴ The correct answer is 3/7.

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