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Answer 1

Step-by-step explanation:

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Answer 2

✰ Solution :

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2. Simplify-

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$\large \rm i) \: \: {2}^{ \frac{2}{3} } \times {2}^{ \frac{1}{5} }$

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• In multiplication when bases are same then the powers are added.

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$\large \rm \implies \: {2}^{ \frac{2}{3} } \times {2}^{ \frac{1}{5} } = {2}^{ \frac{2}{3} + \frac{1}{5} }$

$\large \implies \rm \: {2}^{ \frac{10 + 3}{15} } = \boxed{ {2}^{ \frac{13}{15} }}$

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$\large \rm \: ii) \: {\left( \dfrac{1}{ {3}^{3} } \right)}^{7}$

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• Powers power = power multiply

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$\large \rm \implies \: {\left( \dfrac{1}{ {3}^{3} } \right)}^{7} = {\left( \dfrac{1}{ {3}^{} } \right)}^{7 \times 3} \\ \\ \\ \large \boxed{ = {\left( \dfrac{1}{ {3}^{} } \right)}^{21} }$

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$\large \rm \: iii) \: \dfrac{ {11}^{ \frac{1}{2} } }{ {11}^{ \frac{1}{4} } }$

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$\large \rm \mapsto \: \: \dfrac{ {11}^{ \frac{1}{2} } }{ {11}^{ \frac{1}{4} } } = {11}^{ \frac{1}{2} } \div {11}^{ \frac{1}{4} }$

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• In division when bases are same then the powers are subtracted.

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$\large \rm \implies {11}^{ \frac{1}{2} } \div {11}^{ \frac{1}{4} } = {11}^{ \frac{1}{2} - \frac{1}{4} }$

$\large \implies \: \rm {11}^{ \frac{2 - 1}{4} } = \boxed{ {11}^{ \frac{1}{4} }}$

$\large \rm \boxed{ = \sqrt[4]{11} }$