Question

KINDLY SOLVE IT WITH EXPLANATION!!
DONT STEAL POINTS ^-^​

Answer 1

Given:

`\sf{\dots\implies{\frac{{9}^(n) * {3}^(2) *({{3}^{(- n)/(2) })}^(- 2) -27^2}{ {3}^(3m)*{2}^(3)}}}`

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What are asked to do?

We need to simply
`\sf{\frac{{9}^(n) * {3}^(2) *({{3}^{(- n)/(2) })}^(- 2) -27^2}{ {3}^(3m)*{2}^(3)}}`.

`\rule{80mm}{1pt}`

Solution:

`\sf{\dots\implies{\frac{{9}^(n) * {3}^(2) *({{3}^{(- n)/(2) })}^(- 2) -(27)^2}{ {3}^(3m)*{2}^(3)}}}`

`\sf{\dots\implies{\frac{{3}^(2n) * {3}^(2) *({{3}^{\frac{ \cancel{- }n}{ \cancel2} })}^{ \cancel{- 2}} -(3^(3) )^(2) }{ {3}^(3m)*{2}^(3)}}}`

`\sf{\dots\implies{\frac{{3}^(2n) * {3}^(2) *({{3)}^(n)} -(3 )^(6) }{ {3}^(3m)*{2}^(3)}}}`

Since the base (3) is same so just add the exponents of multiple one.

`\sf{\dots\implies{\frac{{3}^((2n + 2 + n))-(3 )^(6) }{ {3}^(3m)*{2}^(3)}}}`

`\sf{\dots\implies{\frac{{3}^((3n + 2))-(3 )^(6) }{ {3}^(3m)*{2}^(3)}}}`

`\sf{\dots\implies{\frac{{3}^((3n + 2))-(27 )^(2) }{ {3}^(3m)*{2}^(3)}}}`

`\sf{\dots\implies{\frac{{3}^((3n + 2))-( {3}^(2) * {9}^(2) )}{ {3}^(3m)*{2}^(3)}}}`

Take 3² as common.

`\sf{\dots\implies{\frac{ {3}^(2)(({3)}^(3n)-9^(2))}{ {3}^(3m) * 8}}}`

Solve the powers.

`\sf{\dots\implies{\frac{ 9({27}^(n)-81)}{ {27}^(m) * 8}}}`

Again take 27 as common.

`\sf{\dots\implies{\frac{ 9 * 27({1}^(n)-3)}{ {27}^(m) * 8}}}`

Answer 2

⚘Refer to the attachment for solution and below for steps!!

`\purple{ \rule{300pt}{3pt}}`

• Write the number in exponential form with the base of 3
• Simplify the expression by multiplying exponents
• Evaluate the power
• Calculate the product
• Use the commutative property to reorder the terms
• Evaluate the power
• And, We are done solving!!~