Solve [(-1,2):(-3)]^3:[(-2)^2]^3

$$[ ( - 1,2 ) : ( - 3 ) ] ^ { 3 } : [ ( - 2 ) ^ { 2 } ] ^ { 3 }$$

Evaluate

$$0,001$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\left(\frac{-1,2}{-3}\right)^{3}}{\left(-2\right)^{6}}$$

Expand \frac{-1,2}{-3} by multiplying both numerator and the denominator by 10.

$$\frac{\left(\frac{-12}{-30}\right)^{3}}{\left(-2\right)^{6}}$$

Reduce the fraction \frac{-12}{-30} to lowest terms by extracting and canceling out -6.

$$\frac{\left(\frac{2}{5}\right)^{3}}{\left(-2\right)^{6}}$$

Calculate \frac{2}{5} to the power of 3 and get \frac{8}{125}.

$$\frac{\frac{8}{125}}{\left(-2\right)^{6}}$$

Calculate -2 to the power of 6 and get 64.

$$\frac{\frac{8}{125}}{64}$$

Express \frac{\frac{8}{125}}{64} as a single fraction.

$$\frac{8}{125\times 64}$$

Multiply 125 and 64 to get 8000.

$$\frac{8}{8000}$$

Reduce the fraction \frac{8}{8000} to lowest terms by extracting and canceling out 8.

$$\frac{1}{1000}$$

Factor

$$\frac{1}{2 ^ {3} \cdot 5 ^ {3}} = 0.001$$