Question

$(-\frac{5}{6}{)}^{3/4}$ when divided by $(-\frac{5}{6}{)}^{7/6}$ becomes $(-\frac{5}{6}{)}^{7-x}$, the value of x is:

• A. $\frac{7}{12}$
• B. $\frac{89}{12}$
• C. $\frac{8}{12}$
• D. $\frac{10}{12}$

Answer 1

The correct option is B $\frac{89}{12}$

$\frac{(-\frac{5}{6}{)}^{3/4}}{(-\frac{5}{6}{)}^{7/6}}=(-\frac{5}{6}{)}^{7-x}$

$\Rightarrow$ $(-\frac{5}{6}{)}^{\frac{3}{4}-\frac{7}{6}}=(-\frac{5}{6}{)}^{7-x}$ ...$[\frac{x^m}{x^n}=x^{m-n}]$

$\Rightarrow$ $(-\frac{5}{6}{)}^{\frac{18-28}{24}}=(-\frac{5}{6}{)}^{7-x}$

$\Rightarrow$ $(-\frac{5}{6}{)}^{\frac{-5}{12}}=(-\frac{5}{6}{)}^{7-x}$

$\Rightarrow$ $\frac{-5}{12}=7-x$

$\Rightarrow$ $x=7+\frac{5}{12}$

$\Rightarrow$ $x=\frac{84+5}{12}$

$\therefore$ $x=\frac{89}{12}$