Solve (11/3)^3:4^2+(2/3)^3:2^9

$$( 1 \frac { 1 } { 3 } ) ^ { 3 } : 4 ^ { 2 } + ( \frac { 2 } { 3 } ) ^ { 3 } : 2 ^ { 9 }$$

Evaluate

$$\frac{257}{1728}\approx 0.148726852$$

Solution Steps

Multiply 1 and 3 to get 3.

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

Add 3 and 1 to get 4.

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

Calculate \frac{4}{3} to the power of 3 and get \frac{64}{27}.

$$\frac{\frac{64}{27}}{4^{2}}+\frac{\left(\frac{2}{3}\right)^{3}}{2^{9}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{\frac{64}{27}}{16}+\frac{\left(\frac{2}{3}\right)^{3}}{2^{9}}$$

Express \frac{\frac{64}{27}}{16} as a single fraction.

$$\frac{64}{27\times 16}+\frac{\left(\frac{2}{3}\right)^{3}}{2^{9}}$$

Multiply 27 and 16 to get 432.

$$\frac{64}{432}+\frac{\left(\frac{2}{3}\right)^{3}}{2^{9}}$$

Reduce the fraction \frac{64}{432} to lowest terms by extracting and canceling out 16.

$$\frac{4}{27}+\frac{\left(\frac{2}{3}\right)^{3}}{2^{9}}$$

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

$$\frac{4}{27}+\frac{\frac{8}{27}}{2^{9}}$$

Calculate 2 to the power of 9 and get 512.

$$\frac{4}{27}+\frac{\frac{8}{27}}{512}$$

Express \frac{\frac{8}{27}}{512} as a single fraction.

$$\frac{4}{27}+\frac{8}{27\times 512}$$

Multiply 27 and 512 to get 13824.

$$\frac{4}{27}+\frac{8}{13824}$$

Reduce the fraction \frac{8}{13824} to lowest terms by extracting and canceling out 8.

$$\frac{4}{27}+\frac{1}{1728}$$

Add \frac{4}{27} and \frac{1}{1728} to get \frac{257}{1728}.

$$\frac{257}{1728}$$

Factor

$$\frac{257}{2 ^ {6} \cdot 3 ^ {3}} = 0.14872685185185186$$