Question

What is the value of \(\frac{{{3^{n + 3}} + {3^2} \times {3^n}}}{{{3^{n + 1}} \times {3^2}}} - {3^{ - 1}}\)?
1. 3² - 3^-2
2. 3^-1 - 3²
3. 3⁰
4. 3^-1

Answer 1

Correct Answer - Option 3 : 3⁰

Formula Used:

a^b × a^c = a^b+c

a⁰ = 1

Calculation:

\(\frac{{{3^{n + 3}} + {3^2} \times {3^n}}}{{{3^{n + 1}} \times {3^2}}} - {3^{ - 1}}\)

⇒ \(\frac{{{3^{n + 3}} + {3^2} \times {3^n}}}{{{3^{n + 1}} \times {3^2}}} - {3^{ - 1}}\) 

⇒  \(\frac{{{3^{n + 1}} [ {3^2+} \ {3]}}}{{{3^{n + 1}} \times {3^2}}} - {3^{ - 1}}\) 

⇒ \(\frac{{{} {9}+ \ {3} }}9 -{3^{ - 1}}\) 

⇒ \( {12 \ \over 9}\) - \( {1\ \over 3}\) 

⇒ \( {12-3 \ \over 9}\) = 1 = 3⁰

∴ The value of \(\frac{{{3^{n + 3}} + {3^2} \times {3^n}}}{{{3^{n + 1}} \times {3^2}}} - {3^{ - 1}}\) is 3⁰.