Question

$9^{\frac{3}{2}}÷(243{)}^{-\frac{2}{3}}$ simplifies to:

• A. $3^{\frac{10}{3}}$
• B. $3^{\frac{19}{3}}$
• C. $3^{\frac{1}{3}}$
• D. $3^{19}$

Answer 1

The correct option is B $3^{\frac{19}{3}}$

The given expression is

$9^{\frac{3}{2}}÷{243}^{-\frac{2}{3}}$

$=9^{\frac{3}{2}}\times {243}^{\frac{2}{3}}$

$={\left(3^2\right)}^{\frac{3}{2}}\times {\left(3^5\right)}^{\frac{2}{3}}$

$=3^3\times 3^{\frac{10}{3}}$

$=3^{3+\frac{10}{3}}$

$=3^{\frac{19}{3}}$