Solve 9^-3:81^2/24^-2:27^2

$$\frac { 9 ^ { - 3 } : 81 ^ { 2 } } { 24 ^ { - 2 } : 27 ^ { 2 } }$$

Evaluate

$$\frac{64}{729}\approx 0.087791495$$

Solution Steps

Divide \frac{9^{-3}}{81^{2}} by \frac{24^{-2}}{27^{2}} by multiplying \frac{9^{-3}}{81^{2}} by the reciprocal of \frac{24^{-2}}{27^{2}}.

$$\frac{9^{-3}\times 27^{2}}{81^{2}\times 24^{-2}}$$

Calculate 9 to the power of -3 and get \frac{1}{729}.

$$\frac{\frac{1}{729}\times 27^{2}}{81^{2}\times 24^{-2}}$$

Calculate 27 to the power of 2 and get 729.

$$\frac{\frac{1}{729}\times 729}{81^{2}\times 24^{-2}}$$

Multiply \frac{1}{729} and 729 to get 1.

$$\frac{1}{81^{2}\times 24^{-2}}$$

Calculate 81 to the power of 2 and get 6561.

$$\frac{1}{6561\times 24^{-2}}$$

Calculate 24 to the power of -2 and get \frac{1}{576}.

$$\frac{1}{6561\times \frac{1}{576}}$$

Multiply 6561 and \frac{1}{576} to get \frac{729}{64}.

$$\frac{1}{\frac{729}{64}}$$

Divide 1 by \frac{729}{64} by multiplying 1 by the reciprocal of \frac{729}{64}.

$$1\times \frac{64}{729}$$

Multiply 1 and \frac{64}{729} to get \frac{64}{729}.

$$\frac{64}{729}$$

Factor

$$\frac{2 ^ {6}}{3 ^ {6}} = 0.0877914951989026$$