9) $left( \frac{16^{\frac{5}{3}}}{16^{\frac{5}{6}}} \right)^{\frac{9}{5}}$

Answer:

$16^{\frac{3}{10}}$

Explanation:

Step1: Subtract exponents in denominator

$\frac{5}{3} - \frac{5}{6} = \frac{10}{6} - \frac{5}{6} = \frac{5}{6}$

Step2: Simplify base to single exponent

$16^{\frac{5}{6}}$

Step3: Multiply outer exponent

$\frac{5}{6} \times \frac{9}{5} = \frac{9}{6} = \frac{3}{10}$

Step4: Write final simplified form

$16^{\frac{3}{10}}$