2^0 + 3^−2 / 3^-1
You asked:
Evaluate the expression: \({2}^{0} + \frac{{3}^{-2}}{{3}^{-1}}\)
MathBot Answer:
\[{2}^{0} + \frac{{3}^{-2}}{{3}^{-1}} = \frac{4}{3} = 1.\overline{3}\]
\[\begin{aligned}{2}^{0} + \frac{{3}^{-2}}{{3}^{-1}}& = 2^{0} + \frac{1}{3^{2}} \cdot \frac{1}{\frac{1}{3}}\\& = 1 + \frac{1}{3^{2}} \cdot \frac{1}{\frac{1}{3}}\\& = 1 + \frac{1}{9} \cdot \frac{1}{\frac{1}{3}}\\& = 1 + \frac{1}{3}\\& = \frac{4}{3}\end{aligned}\]