Sabaivandainnocenthoidn
Answered

IDNLearn.com connects you with a community of knowledgeable individuals ready to help. Whether it's a simple query or a complex problem, our community has the answers you need.

ans : 27.......................

[tex] \frac{(243 {)}^{2n/5} . {3}^{2n + 1} }{ {9}^{n + 1}. {3}^{2(n - 2)} } \\ [/tex]

please give step by step explanation...
​

Sagot :

DᴀʀᴋPᴀʀᴀᴅᴏxidn

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex]\qquad \sf  \dashrightarrow \: \dfrac{((243 {)}^{2n/5} ) \sdot( {3}^{2n + 1}) }{ ({9}^{n + 1}) \sdot( {3}^{2(n - 2)} )}[/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{(3{)}^{5(2n/5)} ) \sdot( {3}^{2n + 1}) }{ ({3 }^{2(n + 1)}) \sdot( {3}^{2(n - 2)} )}[/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{(3{)}^{2n} \sdot( {3}^{2n + 1}) }{ ({3 }^{(2n + 2)}) \sdot( {3}^{(2n - 4)} )}[/tex]

let's break it up :

  • [tex] \sf  3 {}^{2n} = (3 {}^{2n -4} ) \sdot(3 {}^{4} )[/tex]
  • [tex] \sf  3 {}^{(2n + 1)} = (3 {}^{2n -4} ) \sdot(3 {}^{5} )[/tex]
  • [tex] \sf  3 {}^{(2n + 2)} = (3 {}^{2n -4} ) \sdot(3 {}^{6} )[/tex]

now let's take [tex]{ \sf {3}^{(2n-4)}} [/tex] common here ~

[tex]\qquad \sf  \dashrightarrow \: \dfrac{(3{)}^{(2n - 4)} (3 {}^{4} \sdot{3}^{5}) }{ {(3 )}^{(2n - 4)}(3 {}^{6} \sdot1)}[/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{{} (3 {}^{4} \sdot{3}^{5}) }{ (3 {}^{6} \sdot1)}[/tex]

[tex]\qquad \sf  \dashrightarrow \: \dfrac{{} 3 {}^{9} }{ 3 {}^{6} }[/tex]

[tex]\qquad \sf  \dashrightarrow \: 3 {}^{3} [/tex]

[tex]\qquad \sf  \dashrightarrow \: 27[/tex]

Hope008idn

Answer:

  • 27

Step-by-step explanation:

[tex]\sf \cfrac{243^{\frac{2n}{5}}\cdot \:3^{2n+1}}{9^{n+1}\cdot \:3^{2\left(n-2\right)}}[/tex]

[tex]\sf 9^{n+1}\cdot \:3^{2\left(n-2\right)}[/tex]

Simplify:-

  • [tex]\sf 3^{4n-2}[/tex]

[tex]\sf \cfrac{3^{2n}\cdot \:3^{2n+1}}{\boxed{\bf 3^{4n-2}}}[/tex]

Now, Factor:-

  • [tex]\sf 243^{\frac{2n}{5}}[/tex]
  • [tex]= \boxed{\bf 3^{2n}}[/tex]

[tex]\sf \cfrac{3^{2n}\cdot \:3^{2n+1}}{3^{4n-2}}[/tex]

Now, let's simplify:-

  • [tex]\sf \cfrac{3^{2n}}{3^{4n-2}}[/tex]
  • [tex]=\boxed{\bf 3^{-2n+2}}[/tex]
  • [tex]\sf 3^{-2n+2}\cdot \:3^{2n+1}[/tex]

Simplify:-

  • [tex]\sf 3^{-2n+2}\cdot \:3^{2n+1}[/tex]

Apply the exponent rule:-

  • [tex]\sf 3^{-2n+2+2n+1}[/tex]
  • [tex]\sf 3^3[/tex]
  • [tex]\sf 27[/tex]

Therefore, your answer is 27.

______________________

Hope this helps!

Have a great day!

We greatly appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. For precise answers, trust IDNLearn.com. Thank you for visiting, and we look forward to helping you again soon.