Question

please give answer properly​

Answer 1

Answer:

1/648

Step-by-step explanation:

I hope it's correct

Answer 2

Given :

$\dfrac{ {(64)}^{ \frac{ - 1}{6} } \times ( {216})^{ \frac{ - 1}{3} } \times ( {81)}^{ \frac{1}{4} } }{( {512)}^{ \frac{ - 1}{3} } \times ( {16)}^{ \frac{1}{4} } \times ( {9)}^{ \frac{ - 1}{2} } }$

To find :

Simplified form

Identity used :

$\sf \bullet \: ( {a}^{m} ) {}^{n} \: = \: ( {a}^{mn})$

$\sf \bullet \: ( {a}^{ - m} ) \: = \: ( \dfrac{1}{ {a}^{m} })$

$\sf \bullet \: ( {a}^{m} ) \times( {a}^{n} ) \: = \: {a}^{(m + n)}$

Solution :

$\dfrac{ {(64)}^{ \frac{ - 1}{6} } \times ( {216})^{ \frac{ - 1}{3} } \times ( {81)}^{ \frac{1}{4} } }{( {512)}^{ \frac{ - 1}{3} } \times ( {16)}^{ \frac{1}{4} } \times ( {9)}^{ \frac{ - 1}{2} } }$

$\sf \implies \: \dfrac{ {( {2}^{6} )}^{ \frac{ - 1}{6} } \times ( { {6}^{3} })^{ \frac{ - 1}{3} } \times ( { {3}^{4} )}^{ \frac{1}{4} } }{( { {8}^{3} )}^{ \frac{ - 1}{3} } \times ( { {2}^{4} )}^{ \frac{1}{4} } \times ( { {3}^{2} )}^{ \frac{ - 1}{2} } }$

$\sf \implies \: \dfrac{ {( 2 )}^{ \frac{ 6 \times (- 1)}{6} } \times ( { {6}})^{ \frac{3 \times ( - 1)}{3} } \times ( { {3} )}^{ 4 \times \frac{1}{4} } }{( { {8} )}^{ \frac{3 \times ( - 1)}{3} } \times ( { {2} )}^{ \frac{4 \times 1}{4} } \times ( { {3} )}^{ \frac{ 2 \times (- 1)}{2} } }$

$\sf \implies \: \dfrac{ {( 2 )}^{ - 1 } \times ( { {6}})^{ - 1 } \times ( { {3} )}^{ 1 } }{( { {8} )}^{ - 1 } \times ( { {2} )}^{ 1 } \times ( { {3} )}^{ - 1} }$

$\sf \implies \: \dfrac{ {( 2 )}^{ - 1 - 1 } \times ( { {6}})^{ - 1 } \times ( { {3} )}^{ 1 - ( - 1)} }{( { {8} )}^{ - 1 } }$

$\sf \implies \: \dfrac{ {( 2 )}^{ - 2 } \times ( { {6}})^{ - 1 } \times ( { {3} )}^{ 2} }{( { {8} )}^{ - 1 } }$

$\sf \implies \: \dfrac{ ( { {8}})^{ 1 } \times ( { {3} )}^{ 2} }{( { {6} )}^{ 1 } \times {(2)}^{2} }$

$\sf \implies \: \dfrac{ 8 \times 9 }{ {6} \times 4 }$

$\sf \implies \: \dfrac{ 72}{24}$

$\sf \implies \: \bold{3}$

ANSWER : 3