Question

Please answer question number 7 from the attachment

Answer 1

Solution :::

$\sqrt[3]{128} = (128)^{ \frac{1}{3} } \\ \\ \sqrt[5]{64} \: = \: (64) ^{ \frac{1}{5} }$
Answer :

For this take LCM :

128 = 2 × 2 × 2 × 2 × 2 × 2 × 2

64 = 2 × 2 × 2 × 2 × 2 × 2

cube roots are as follows

$\sqrt[3]{128} = 2 \times 2 \times \sqrt[3]{2} = 4 \sqrt[3]{2}$

$\sqrt[5]{64} = 2 \times 2 = 2\sqrt[5]{2}$

$\dfrac{ \sqrt[3]{128} }{ \sqrt[5]{64} } = \dfrac{4 \sqrt[3]{2} }{2\sqrt[5]{2}}$

By using exponential formula

$2.(2)^{\frac{1}{3}-\frac{1}{5}} \: = \: 2.(2)^{\frac{5-3}{15}} \: = \: 2.2^{\frac{2}{15}}$

$= \: 2^{\frac{2}{15}+1} \\ = \: 2^{\frac{17}{15}}$