Question

3^n.3^2n+1
_________
9^n.3 ^n-1​

Answer 1

Required Answer:-

Given to evaluate:

• $\sf \dfrac{ {3}^{n} \times {3}^{2n + 1} }{ {9}^{n} \times {3}^{n - 1} }$

Solution:

We have,

$\sf \dfrac{ {3}^{n} \times {3}^{2n + 1} }{ {9}^{n} \times {3}^{n - 1} }$

$\sf = \dfrac{ {3}^{n} \times {3}^{2n + 1} }{ {( {3}^{2} )}^{n} \times {3}^{n - 1} }$

$\sf = \dfrac{ {3}^{n} \times {3}^{2n + 1} }{{3}^{2n} \times {3}^{n - 1} } \: \: \blue{ \bigg( ({x}^{m})^{n} = {x}^{mn} \bigg)}$

$\sf = \dfrac{ {3}^{n + 2n + 1} }{{3}^{2n + n - 1} } \: \: \blue{ \bigg( {x}^{m} \times x^{n} = {x}^{m + n} \bigg)}$

$\sf = \dfrac{ {3}^{3n + 1} }{{3}^{3n- 1} }$

$\sf = {3}^{(3n + 1) - (3n - 1)} \: \: \blue{\bigg( \dfrac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \bigg) }$

$\sf = {3}^{2}$

$\sf = 9$

★ Hence, the simplified form of the expression is - 9.

Answer:

• Simplified form is - 9.

Answer 2

Answer:

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Step-by-step explanation: