Question

write 3n/9n-1 as a power of 3
URGENT!!! HELP!

Answer 1

$\displaystyle \sf{ \frac{ {3}^{n} }{ {9}^{n - 1} } } = {3}^{2 - n}$

Given :

$\displaystyle \sf{ \frac{ {3}^{n} }{ {9}^{n - 1} } }$

To find :

To express as a power of 3

Formula :

$\displaystyle \sf{1. \: \: \: \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }$

$\displaystyle \sf{2. \: \: \: { ({a}^{m} )}^{n} = {a}^{mn} }$

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ \frac{ {3}^{n} }{ {9}^{n - 1} } }$

Step 2 of 2 :

Express as power of 3

$\displaystyle \sf{ \frac{ {3}^{n} }{ {9}^{n - 1} } }$

$\displaystyle \sf{ = \frac{ {3}^{n} }{ {( {3}^{2} )}^{n - 1} } }$

$\displaystyle \sf{ = \frac{ {3}^{n} }{ {3}^{(2 \times (n - 1))} } }\: \: \: \bigg[ \: \because \:{ ({a}^{m} )}^{n} = {a}^{mn} \bigg]$

$\displaystyle \sf{ = \frac{ {3}^{n} }{ {3}^{2n - 2} } }$

$\displaystyle \sf{ = {3}^{n - 2n + 2} }\: \: \: \bigg[ \: \because \:\frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} \bigg]$

$\displaystyle \sf{ = {3}^{2 - n} }$

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Answer 2

Answer:

Step-by-step explanation: