Question

simplify the following​

Answer 1

$\sf \colorbox{pink} {Ans.a}$

$\sf \colorbox{god} {Given:-} \: \frac{ {3}^{4} \times ( - 5 {)}^{ - 4} }{9 \times ( {5}^{2} {)}^{3} }$

$\text{To Find:- Value}$

$\sf \colorbox{god} {Formula:- } ( {a}^{ - m} = \frac{1}{ {a}^{m} } )$

Solve:-

$⇒ \frac{ {3}^{4} \times 1}{ {3}^{2} \times (5 {)}^{6} \times ( - 5 {)}^{4} }$

$⇒ \frac{ {3}^{4} \times 1}{ {3}^{2} \times (5 {)}^{6} \times ( - 5 {)}^{4} }$

$⇒ \frac{ {3}^{4 - 2} }{(5 {)}^{6} \times ( - 1 {)}^{4} (5 {)}^{4} } \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ( {a}^{ - m} = \frac{1}{ {a}^{m} } )$

$⇒ \frac{ {3}^{2} }{(5 {)}^{6 + 4} \times 1} = \frac{ {3}^{2} }{ {5}^{10} }$

$\sf \colorbox{pink} {Ans.c}$

$\sf \colorbox{god} {Given:-} \frac{ {3}^{0} + ( {5}^{2} {)}^{3} - {6}^{2} }{( {3}^{2} {)}^{3} \times {5}^{2} }$

$\text{To Find:- Value}$

Solve:-

$⇒\frac{ {3}^{0} + ( {5}^{2} {)}^{3} - {6}^{2} }{( {3}^{2} {)}^{3} \times {5}^{2} } = \frac{1 + {5}^{6} - {6}^{2} }{ {3}^{6} \times {5}^{2} }$

$[\sf \colorbox{god} {➧Using}( {a}^{m} {)}^{n} = {a}^{m \times n} ]$

$⇒ \frac{1 + 15625 - 36}{729 \times 25} = \frac{15590}{18225}$

$= 3118/3645$

$\\ \\ \\ \\ \sf \colorbox{lightgreen} {\red★ANSWER ᵇʸɴᴀᴡᴀʙ}$