Question

Answer this question and if you don't know how to then Don't wait for your answer to be reported​

Answer 1

${\huge{\bf{\red{\underline{Solution:}}}}}$

${\bf{\blue{\underline{Given:}}}}$

${\star \: {\sf{ \: \bigg[ \frac{1}{ {(27)}^{ \frac{ - 1}{3} } } + \frac{1}{ {(625)}^{ \frac{ - 1}{4} } } \bigg] }}}$

${\bf{\blue{\underline{Concept\:Used:}}}}$

$\star{\sf{ \: \: \: {x}^{ \frac{p}{q} } = {x}^{p \times \frac{1}{q} } }}$

$\implies{\sf{ \: \: \: {x}^{ \frac{p}{q} } = {[(x)^{p} ]}^{ \frac{1}{q} } }}$

$\star{\sf{ \: \: \: {x}^{ m} = \frac{1}{ {x}^{-m} } }}$

${\bf{\blue{\underline{Now:}}}}$

we know that ,

• (3)³=27
• (5)⁴=625

$: \implies{\sf{ \frac{1}{[( {3)}^{3}] ^{ \frac{ - 1}{3} } } + \frac{1}{[( {5)}^{4} ]^{ \frac{ - 1}{4} } } }}$

$: \implies{\sf{ \frac{1}{(3) ^{ \frac{ - 3}{3} } } + \frac{1}{(5) ^{ \frac{ - 4}{4} } } }}$

$: \implies{\sf{ \frac{1}{(3) ^{ - 1 } } + \frac{1}{(5) ^{ - 1} } }}$

$: \implies{\sf{ 3 + 5 }}$

$: \implies{\sf{ 8 \: Ans}}$

Answer 2

$Given \: \frac{1}{(27)^{\frac{-1}{3}} }+ \frac{1}{625)^{\frac{-1}{4}}}$

$= (27)^{\frac{1}{3}} + (625)^{\frac{1}{4}}$

_________________

By Exponential Law :

$\blue { \frac{1}{a^{-n}} = a^{n} }$

__________________

$= (3^{3})^{\frac{1}{3}}+ (5^{4})^{\frac{1}{4}}$

$= (3)^{3 \times \frac{1}{3}}+ (5)^{4 \times \frac{1}{4}}$

_________________

By Exponential Law :

$\pink {( a^m)^{n} = a^{m \times n} }$

__________________

$= 3 + 5 \\= 8$

Therefore.,

$\red{\frac{1}{(27)^{\frac{(-1)}{3}}} + \frac{1}{(625)^{\frac{(-1)}{4}}}}$

$\green {= 8}$

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