Question

please answer this question (simplify) ​

Answer 1

Answer:

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Answer 2

Ans.(i)

$⇒ {2}^{ \frac{2}{3} } , {2}^{ \frac{1}{5} } = {2}^{ \frac{2}{3} + \frac{1}{5} } = {2}^{ \frac{10 + 3}{15} } = {2}^{ \frac{13}{15} }$

Ans.(ii)

$⇒ { \left( \frac{1}{ {3}^{3} } \right) \]}^{7} = { \left( \frac{1}{3} \right) \]}^{3 \times 7} = { \left( \frac{1}{3} \right) \]}^{4}$

$\[ \left[ ∴( {x}^{m} {)}^{n} = {x}^{mn} \right] \]$

$⇒ { \left( \frac{1}{3} \right) \]}^{21}$

Ans.(iii)

$⇒\frac{ {11}^{ \frac{1}{2} } }{ {11}^{ \frac{1}{4} } }$

$\[ \left[ ∴ {a}^{m} \div {a}^{n} = {a}^{m - n} \right] \]$

$⇒ {11}^{ \frac{1}{2} } \div {11}^{ \frac{1}{4} }$

$⇒ {11}^{ \frac{1}{2} - \frac{1}{4} }$

$⇒ {11}^{ \frac{2 - 1}{4} }$

$⇒ {11}^{ \frac{1}{4} }$

Ans.(iv)

$⇒ {7}^{ \frac{1}{2} } . {8}^{ \frac{1}{2} }$

$= \sqrt{7} \times \sqrt{8}$

$= \sqrt{7} \times \sqrt{4 \times 2}$

$= \sqrt{7} \times 2 \times \sqrt{2}$

$= 2.64 \times 2 \times 1.414$

$⇒ {7}^{ \frac{1}{2} } . {8}^{ \frac{1}{2} } = 7.46592$

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