Question

(25)${}^{7.5}$ x (5)${}^{2.5}$ $÷$ (125)${}^{1.5}$ = 5${}^{?}$

• A. 8.5
• B. 13
• C. 16
• D. 17.5
• E. None of these

Answer 1

The correct option is B

13

$\begin{array}{c}Let{\left(25\right)}^{7.5}\times {\left(5\right)}^{2.5}÷{\left(125\right)}^{1.5}=5x.Then,\frac{{\left(5^2\right)}^{7.5}\times {\left(5\right)}^{2.5}}{{\left(5^3\right)}^{1.5}}=5x\iff \frac{5^{\left(2\times 7.5\right)}\times 5^{2.5}}{5^{\left(3\times 1.5\right)}}=5^x\\ \iff \frac{5^{15}\times 5^{2.5}}{5^{4.5}}=5^x\iff 5^{\left(15+2.5-4.5\right)}=5^{13}\iff x=13.\end{array}$