Question

3 to the power 1 + 3 to the power minus 1 + 3 to the power two + 3 to the power minus 2​

Answer 1

Question :

${3}^{1} + {3}^{-1} + {3}^{2} + {3}^{-2}$

Identity used :

${a}^{-b} \: = \dfrac{1}{{a}^{b}}$

{whenever the power is in negative , the number will be converted to its reciprocal }

Solution :

${3}^{1} + {3}^{-1} + {3}^{2} + {3}^{-2} \\ \\ \implies \: 3 \: + \frac{1}{ {3}^{1} } + {3}^{2} +\frac{1}{ {3}^{2} } \\ \\ \implies 3 + 9 + \frac{1}{3} + \: \frac{1}{9} \\ \\ \implies 12 + \frac{1}{3} + \frac{1}{9} \\ \\ taking \: lcm \\ \implies \dfrac{(12\times 9) + (1\times3) + (1 \times 1) }{9} \\ \\ \implies \dfrac{(108 + 3 + 1)}{9} \\ \\ \implies \dfrac{112}{9}$

Important point used :

• 3¹ = 3
• 3² = 9

Answer : $\dfrac{112}{9}$