Question

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

• 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 $\frac{3}{7}$

$\frac{{\left(243\right)}^{0.13}\times {\left(243\right)}^{0.07}}{{\left(7\right)}^{0.25}\times {\left(49\right)}^{0.075}\times {\left(343\right)}^{0.2}}$
= $\frac{{\left(243\right)}^{0.13+0.07}}{{\left(7\right)}^{0.25}\times {\left(7^2\right)}^{0.075}\times {\left(7^3\right)}^{0.2}}$
= $\frac{{\left(3^5\right)}^{0.20}}{7^{0.25+0.15+0.60}}=\frac{3^1}{7^1}=\frac{3}{7}$