Question

Simplify:

$[{\left(2\frac{10}{27}\right)}^{-\frac{2}{3}}÷{\left(11\frac{1}{9}\right)}^{-0.5}]+[{\left(6.25\right)}^{0.5}÷{(-4)}^{-1}]$

• A. $-8\frac{1}{8}$
• B. $8\frac{1}{8}$
• C. $1\frac{7}{8}$
• D. $-1\frac{7}{8}$

Answer 1

The correct option is A $-8\frac{1}{8}$

Given exp $=[{\left(\frac{64}{27}\right)}^{-\frac{2}{3}}÷{\left(\frac{100}{9}\right)}^{-\frac{1}{2}}]+\left[\right(6.25{)}^{\frac{1}{2}}÷\frac{1}{-4}]$
$=[{\left({\left(\frac{4}{3}\right)}^3\right)}^{-\frac{2}{3}}÷{\left({\left(\frac{10}{3}\right)}^2\right)}^{-\frac{1}{2}}]+[{\left({\left(2.5\right)}^2\right)}^{\frac{1}{2}}÷\frac{1}{-4}]$
$=[{\left(\frac{4}{3}\right)}^{-2}÷{\left(\frac{10}{3}\right)}^{-1}]+2.5\times -4$
$=[{\left(\frac{3}{4}\right)}^2÷\frac{3}{10}]-10=\frac{9}{16}\times \frac{10}{3}-10$
$=\frac{15}{8}-10=\frac{15-80}{8}=\frac{-65}{8}=-8\frac{1}{8}$