Question

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 :

• A.
• B.
• C.
• D.
• E.

Answer 1

The correct option is A

$\begin{array}{c}\frac{{\left(243\right)}^{0.13}\times {\left(243\right)}^{0.07}}{{\left(7\right)}^{0.25}\times {\left(49\right)}^{0.075}\times {\left(343\right)}^{0.2}}=\frac{{\left(243\right)}^{\left(0.13+0.07\right)}}{7^{0.25}\times {\left(7^2\right)}^{0.075}\times {\left(7^3\right)}^{0.2}}\\ =\frac{{\left(243\right)}^{0.2}}{7^{0.25}\times 7^{\left(2\times 0.075\right)}\times 7^{(3\times 0.2)}}=\frac{{\left(3^5\right)}^{0.2}}{7^{0.25}\times 7^{0.15}\times 7^{0.6}}\\ =\frac{3^{\left(5\times 0.2\right)}}{7^{\left(0.25+0.15+0.6\right)}}=\frac{3^1}{7^1}=\frac{3}{7}.\end{array}$