Question

guys Please answer this, it's urgent.....​

Answer 1

(a) Solution:

=> $\frac{1}{ \sqrt{7} + \: \sqrt{5}}$

=> $\frac{1}{ \sqrt{7} + \sqrt{5} } \times \frac{ \sqrt{7} - \sqrt{5} }{ \sqrt{7} - \sqrt{5} }$

=> $\frac{ \sqrt{7} - \sqrt{5} }{( \sqrt{7}) ^{2} - (\sqrt{5})^{2}}$ [By using the identity (a+b)(a-b) = a² - b² ]

=> $\frac{ \sqrt{7} - \sqrt{5}}{7 - 5} = \frac{ \sqrt{7} - \sqrt{5} \: }{2}$

$Hence, \: \frac{ \sqrt{7} - \sqrt{5}}{2} \: is \: your \: answer$

Answer 2

(a) Solution:

=> $\frac{1}{ \sqrt{7} + \: \sqrt{5}}$

=> $\frac{1}{ \sqrt{7} + \sqrt{5} } \times \frac{ \sqrt{7} - \sqrt{5} }{ \sqrt{7} - \sqrt{5} }$

=> $\frac{ \sqrt{7} - \sqrt{5} }{( \sqrt{7}) ^{2} - (\sqrt{5})^{2}}$ [ By using the identity (a+b)(a-b) = a² - b² ]

=> $\frac{ \sqrt{7} - \sqrt{5}}{7 - 5} = \frac{ \sqrt{7} - \sqrt{5} \: }{2}$

$Hence, \: \frac{ \sqrt{7} - \sqrt{5}}{2} \: is \: your \: answer$

(b) Solution:

by using the exponent rule that is $a^{n} + a^{m} = a^{n + m}$

we get:

=> $( {2}^{ \frac{4}{3} })( {2}^{ \frac{3}{5} } ) = {2}^{ \frac{4}{3} + \frac{3}{5} }$

taking LCM we get,

=> ${2}^{ \frac{20 + 9}{3 \times 5} } = {2}^{ \frac{29}{15} }$

$Hence, \: ( {2}^{ \frac{29}{15} } ) \: is \: your \: answer$

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At last (╥﹏╥)

I had to answer from this ID (╥﹏╥)