Solve {left(4/3^2right)}^-2{left(3^-2/2^-1right)}^3+23^-1

$${ \left( \frac{ 4 }{ { 3 }^{ 2 } } \right) }^{ -2 } { \left( \frac{ { 3 }^{ -2 } }{ { 2 }^{ -1 } } \right) }^{ 3 } +2 { 3 }^{ -1 }$$

Evaluate

$$\frac{13}{18}\approx 0.722222222$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\left(\frac{4}{9}\right)^{-2}\times \left(\frac{3^{-2}}{2^{-1}}\right)^{3}+2\times 3^{-1}$$

Calculate \frac{4}{9} to the power of -2 and get \frac{81}{16}.

$$\frac{81}{16}\times \left(\frac{3^{-2}}{2^{-1}}\right)^{3}+2\times 3^{-1}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{81}{16}\times \left(\frac{\frac{1}{9}}{2^{-1}}\right)^{3}+2\times 3^{-1}$$

Calculate 2 to the power of -1 and get \frac{1}{2}.

$$\frac{81}{16}\times \left(\frac{\frac{1}{9}}{\frac{1}{2}}\right)^{3}+2\times 3^{-1}$$

Divide \frac{1}{9} by \frac{1}{2} by multiplying \frac{1}{9} by the reciprocal of \frac{1}{2}.

$$\frac{81}{16}\times \left(\frac{1}{9}\times 2\right)^{3}+2\times 3^{-1}$$

Multiply \frac{1}{9} and 2 to get \frac{2}{9}.

$$\frac{81}{16}\times \left(\frac{2}{9}\right)^{3}+2\times 3^{-1}$$

Calculate \frac{2}{9} to the power of 3 and get \frac{8}{729}.

$$\frac{81}{16}\times \frac{8}{729}+2\times 3^{-1}$$

Multiply \frac{81}{16} and \frac{8}{729} to get \frac{1}{18}.

$$\frac{1}{18}+2\times 3^{-1}$$

Calculate 3 to the power of -1 and get \frac{1}{3}.

$$\frac{1}{18}+2\times \frac{1}{3}$$

Multiply 2 and \frac{1}{3} to get \frac{2}{3}.

$$\frac{1}{18}+\frac{2}{3}$$

Add \frac{1}{18} and \frac{2}{3} to get \frac{13}{18}.

$$\frac{13}{18}$$

Factor

$$\frac{13}{2 \cdot 3 ^ {2}} = 0.7222222222222222$$