Question

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. \(\frac{4}{5}\)

Answer 1

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

Concepts used:

(am)n = a(m × n)

am × an  = 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) ÷ (7^0.25 × 7^0.15 × 7^0.6)]

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

⇒ (3^1.0 ÷ 7^1.0)

⇒ 3/7

∴ The correct answer is 3/7.