Solve 331/3*(-0.1)^2div(-2.4)^2div[41/6*(-0.2)^0]

$$33 \frac { 1 } { 3 } \times ( - 0.1 ) ^ { 2 } \div ( - 2.4 ) ^ { 2 } \div [ 4 \frac { 1 } { 6 } \times ( - 0.2 ) ^ { 0 } ]$$

Evaluate

$$\frac{1}{72}\approx 0.013888889$$

Solution Steps

Multiply 33 and 3 to get 99.

$$\frac{\frac{\frac{99+1}{3}\left(-0.1\right)^{2}}{\left(-2.4\right)^{2}}}{\frac{4\times 6+1}{6}\left(-0.2\right)^{0}}$$

Add 99 and 1 to get 100.

$$\frac{\frac{\frac{100}{3}\left(-0.1\right)^{2}}{\left(-2.4\right)^{2}}}{\frac{4\times 6+1}{6}\left(-0.2\right)^{0}}$$

Calculate -0.1 to the power of 2 and get 0.01.

$$\frac{\frac{\frac{100}{3}\times 0.01}{\left(-2.4\right)^{2}}}{\frac{4\times 6+1}{6}\left(-0.2\right)^{0}}$$

Multiply \frac{100}{3} and 0.01 to get \frac{1}{3}.

$$\frac{\frac{\frac{1}{3}}{\left(-2.4\right)^{2}}}{\frac{4\times 6+1}{6}\left(-0.2\right)^{0}}$$

Calculate -2.4 to the power of 2 and get 5.76.

$$\frac{\frac{\frac{1}{3}}{5.76}}{\frac{4\times 6+1}{6}\left(-0.2\right)^{0}}$$

Express \frac{\frac{1}{3}}{5.76} as a single fraction.

$$\frac{\frac{1}{3\times 5.76}}{\frac{4\times 6+1}{6}\left(-0.2\right)^{0}}$$

Multiply 3 and 5.76 to get 17.28.

$$\frac{\frac{1}{17.28}}{\frac{4\times 6+1}{6}\left(-0.2\right)^{0}}$$

Expand \frac{1}{17.28} by multiplying both numerator and the denominator by 100.

$$\frac{\frac{100}{1728}}{\frac{4\times 6+1}{6}\left(-0.2\right)^{0}}$$

Reduce the fraction \frac{100}{1728} to lowest terms by extracting and canceling out 4.

$$\frac{\frac{25}{432}}{\frac{4\times 6+1}{6}\left(-0.2\right)^{0}}$$

Multiply 4 and 6 to get 24.

$$\frac{\frac{25}{432}}{\frac{24+1}{6}\left(-0.2\right)^{0}}$$

Add 24 and 1 to get 25.

$$\frac{\frac{25}{432}}{\frac{25}{6}\left(-0.2\right)^{0}}$$

Calculate -0.2 to the power of 0 and get 1.

$$\frac{\frac{25}{432}}{\frac{25}{6}\times 1}$$

Multiply \frac{25}{6} and 1 to get \frac{25}{6}.

$$\frac{\frac{25}{432}}{\frac{25}{6}}$$

Divide \frac{25}{432} by \frac{25}{6} by multiplying \frac{25}{432} by the reciprocal of \frac{25}{6}.

$$\frac{25}{432}\times \frac{6}{25}$$

Multiply \frac{25}{432} and \frac{6}{25} to get \frac{1}{72}.

$$\frac{1}{72}$$

Factor

$$\frac{1}{2 ^ {3} \cdot 3 ^ {2}} = 0.013888888888888888$$