Question

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

Answer 1

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

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• 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!!~

Answer 2

Given:

$\sf{\dots\implies{\dfrac{{9}^{n} \times {3}^{2} \times({{3}^{\frac{- n}{2} })}^{- 2} -27^2}{ {3}^{3m}\times{2}^{3}}}}$

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What are asked to do?

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

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Solution:

$\sf{\dots\implies{\dfrac{{9}^{n} \times {3}^{2} \times({{3}^{\frac{- n}{2} })}^{- 2} -(27)^2}{ {3}^{3m}\times{2}^{3}}}}$

$\sf{\dots\implies{\dfrac{{3}^{2n} \times {3}^{2} \times({{3}^{\frac{ \cancel{- }n}{ \cancel2} })}^{ \cancel{- 2}} -(3^{3} )^{2} }{ {3}^{3m}\times{2}^{3}}}}$

$\sf{\dots\implies{\dfrac{{3}^{2n} \times {3}^{2} \times({{3)}^{n}} -(3 )^{6} }{ {3}^{3m}\times{2}^{3}}}}$

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

$\sf{\dots\implies{\dfrac{{3}^{(2n + 2 + n)}-(3 )^{6} }{ {3}^{3m}\times{2}^{3}}}}$

$\sf{\dots\implies{\dfrac{{3}^{(3n + 2)}-(3 )^{6} }{ {3}^{3m}\times{2}^{3}}}}$

$\sf{\dots\implies{\dfrac{{3}^{(3n + 2)}-(27 )^{2} }{ {3}^{3m}\times{2}^{3}}}}$

$\sf{\dots\implies{\dfrac{{3}^{(3n + 2)}-( {3}^{2} \times {9}^{2} )}{ {3}^{3m}\times{2}^{3}}}}$

Take 3² as common.

$\sf{\dots\implies{\dfrac{ {3}^{2}(({3)}^{3n}-9^{2})}{ {3}^{3m} \times 8}}}$

Solve the powers.

$\sf{\dots\implies{\dfrac{ 9({27}^{n}-81)}{ {27}^{m} \times 8}}}$

Again take 27 as common.

$\sf{\dots\implies{\dfrac{ 9 \times 27({1}^{n}-3)}{ {27}^{m} \times 8}}}$