Question

Solve:

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

• A. $3^{\frac{10}{3}}$
• B. $3^{3^{\frac{13}{3}}}$
• C. $3^{\frac{1}{3}}$
• D. $3^{19}$

Answer 1

The correct option is B

$3^{3^{\frac{13}{3}}}$

Consider the given expression,

$\Rightarrow 9^{\frac{3}{2}÷{\left(243\right)}^{-\frac{2}{3}}}=9^{\frac{3}{2}\times {\left(243\right)}^{\frac{2}{3}}}$

$=9^{\frac{3}{2}\times {\left(3^5\right)}^{\frac{2}{3}}}=9^{\frac{3}{2}\times 3^{\frac{10}{3}}}$

$={\left(3^2\right)}^{\frac{3}{2}\times 3^{\frac{10}{3}}}={\left(3\right)}^{3\times 3^{\frac{10}{3}}}$

$=3^{3^{1+\frac{10}{3}}}=3^{3^{\frac{13}{3}}}$

Hence, this is the answer.