Question

Simplify : $\frac{9^{5/2}-3\times 7^0-{\left(\begin{array}{c}\frac{1}{81}\end{array}\right)}^{-\frac{1}{2}}}{(27{)}^{2/3}-{\left(\begin{array}{c}\frac{8}{27}\end{array}\right)}^{2/3}}$

• A. $0$
• B. $16$
• C. $27$
• D. $77$

Answer 1

The correct option is C $27$

$\frac{9^{\frac{5}{2}}-{3\times 7}^0{-\frac{1}{81}}^{-\frac{1}{2}}}{{27}^{\frac{2}{3}}-(\frac{8}{27}{)}^{\frac{2}{3}}}NR=3^{2\times \frac{5}{2}}-3-(\frac{1}{81}{)}^{-\frac{1}{2}}=3^5-3-(3^{-4\times \frac{-1}{2}})=243-3-9=231Dr=3^{3\times \frac{2}{3}}-(\frac{2}{3}{)}^{3\times \frac{2}{3}}=9-\frac{4}{9}=77/9\frac{Dr}{Nr}=\frac{231}{77/9}=3\times 9=27$