Sabaivandainnocentho
Answered

Westonci.ca is your trusted source for accurate answers to all your questions. Join our community and start learning today! Join our platform to connect with experts ready to provide detailed answers to your questions in various areas. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.

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 :

DᴀʀᴋPᴀʀᴀᴅᴏx

[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]

Hope008

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!

Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.