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The value of \( \Large \frac{ \left(243\right)^{0.13} \times \left(243\right)^{0.07} }{ \left(7\right)^{0.25} \times \left(49\right)^{0.075} \times \left(343\right)^{0.2} } \)

A) \( \Large \frac{3}{7} \)
B) \( \Large \frac{7}{3} \)
C) \( \Large 1\frac{3}{7} \)
D) \( \Large 2\frac{2}{7} \)

Correct Answer:

A) \( \Large \frac{3}{7} \)

Description for Correct answer:
\( \Large \frac{ \left(243\right)^{0.13} \times \left(243\right)^{0.07} }{ \left(7\right)^{0.25} \times \left(49\right)^{0.075} \times \left(343\right)^{0.2} } \)

=\( \Large \frac{243^{0.13+0.07}}{7^{0.25} \times 7^{2 \times 0.75} \times 7^{3 \times 0.2}} \)

=\( \Large \frac{3^{5 \times 0.20}}{7^{0.25+0.150+0.6}} =\frac{3^{1}}{7^{1}} = \frac{3}{7}\)

Part of solved Indices and Surd questions and answers : >> Elementary Mathematics >> Indices and Surd

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