Question

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

• 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 $\frac{3}{7}$

Given, $\frac{(243{)}^{0.13}\times (243{)}^{0.07}}{(7{)}^{0.25}\times (49{)}^{0.075}\times (343{)}^{0.2}}$

$\Rightarrow$ $\frac{(243{)}^{0.13+0.07}}{(7{)}^{0.25}\times (7^2{)}^{0.075}\times (7^3{)}^{0.2}}$

$\Rightarrow$ $\frac{(243{)}^{0.2}}{7^{0.25}\times 7^{2\times 0.075}\times 7^{3\times 0.2}}$

$\Rightarrow$ $\frac{(3^5{)}^{0.2}}{7^{0.25}\times 7^{0.15}\times 7^{0.6}}$

$\Rightarrow$ $\frac{3^{5\times 0.2}}{7^{0.25+0.15+0.6}}$

$\Rightarrow$ $\frac{3^1}{7^1}$

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