Question

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

• A. $\frac{3}{7}$
• B. $\frac{7}{3}$
• C. $1\frac{3}{7}$
• D. $2\frac{2}{7}$

Answer 1

The correct option is A $\frac{3}{7}$

$\frac{(243{)}^{0.13}\times (243{)}^{0.07}}{(7{)}^{0.25}\times (49{)}^{0.075}\times (343{)}^{0.2}}$ $=\frac{(3^5{)}^{0.13}\times (3^5{)}^{0.07}}{(7{)}^{0.25}\times (7^2{)}^{0.075}\times (7^3{)}^{0.2}}$

$=\frac{(3{)}^{0.65}\times (3{)}^{0.35}}{(7{)}^{0.25}\times (7{)}^{0.15}\times (7{)}^{0.6}}$

$=\frac{(3{)}^{0.65+0.35}}{(7{)}^{0.25+0.15+0.6}}$ ...$[a^m\times a^n=a^{m+n}]$

$\frac{(243{)}^{0.13}\times (243{)}^{0.07}}{(7{)}^{0.25}\times (49{)}^{0.075}\times (343{)}^{0.2}}$ $=\frac{3^1}{7^1}$