Solve (3^{-1}-4^-7)^-1+(-3)^-2:(-2/3)^-3

$$( 3 ^ { - 1 } - 4 ^ { - 7 } ) ^ { - 1 } + ( - 3 ) ^ { - 2 } : ( - \frac { 2 } { 3 } ) ^ { - 3 }$$

Evaluate

$$\frac{11812888}{3980583}\approx 2.967627606$$

Solution Steps

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

$$\left(\frac{1}{3}-4^{-7}\right)^{-1}+\frac{\left(-3\right)^{-2}}{\left(-\frac{2}{3}\right)^{-3}}$$

Calculate 4 to the power of -7 and get \frac{1}{16384}.

$$\left(\frac{1}{3}-\frac{1}{16384}\right)^{-1}+\frac{\left(-3\right)^{-2}}{\left(-\frac{2}{3}\right)^{-3}}$$

Subtract \frac{1}{16384} from \frac{1}{3} to get \frac{16381}{49152}.

$$\left(\frac{16381}{49152}\right)^{-1}+\frac{\left(-3\right)^{-2}}{\left(-\frac{2}{3}\right)^{-3}}$$

Calculate \frac{16381}{49152} to the power of -1 and get \frac{49152}{16381}.

$$\frac{49152}{16381}+\frac{\left(-3\right)^{-2}}{\left(-\frac{2}{3}\right)^{-3}}$$

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

$$\frac{49152}{16381}+\frac{\frac{1}{9}}{\left(-\frac{2}{3}\right)^{-3}}$$

Calculate -\frac{2}{3} to the power of -3 and get -\frac{27}{8}.

$$\frac{49152}{16381}+\frac{\frac{1}{9}}{-\frac{27}{8}}$$

Divide \frac{1}{9} by -\frac{27}{8} by multiplying \frac{1}{9} by the reciprocal of -\frac{27}{8}.

$$\frac{49152}{16381}+\frac{1}{9}\left(-\frac{8}{27}\right)$$

Multiply \frac{1}{9} and -\frac{8}{27} to get -\frac{8}{243}.

$$\frac{49152}{16381}-\frac{8}{243}$$

Subtract \frac{8}{243} from \frac{49152}{16381} to get \frac{11812888}{3980583}.

$$\frac{11812888}{3980583}$$

Factor

$$\frac{2 ^ {3} \cdot 857 \cdot 1723}{3 ^ {5} \cdot 16381} = 2\frac{3851722}{3980583} = 2.96762760630792$$