Question

(18)${}^{3.5}$ $÷$ (27)${}^{3.5}$x 6${}^{3.5}$ = 2${}^{?}$ .

• A. 3.5
• B. 4.5
• C. 6
• D. 7
• E. 2.5

Answer 1

The correct option is D

7

$\begin{array}{c}{\left(18\right)}^{3.5}÷{\left(27\right)}^{3.5}\times 6^{3.5}=2^x\\ \iff {\left(18\right)}^{3.5}\times \frac{1}{{\left(27\right)}^{3.5}}\times 6^{3.5}=2^x\iff {\left(3^2\times 2\right)}^{3.5}\times \frac{1}{{\left(3^3\right)}^{3.5}}\times {\left(2\times 3\right)}^{3.5}=2^x\\ \iff 3^{\left(2\times 3.5\right)}\times 2^{3.5}\times \frac{1}{3^{\left(3\times 3.5\right)}}\times 2^{3.5}\times 3^{3.5}=2^x\\ \iff 3^7\times 2^{3.5}\times \frac{1}{3^{10.5}}\times 2^{3.5}\times 3^{3.5}=2^x\iff 2^7=2^x\iff x=7.\end{array}$