Solve 3^2/2-sqrt[4]{1/256}+sqrt[3]{-8/64}+{left(1/3right)}^3

$$\frac{ { 3 }^{ 2 } }{ 2 } - \sqrt[ 4 ]{ \frac{ 1 }{ 256 } } + \sqrt[ 3 ]{ \frac{ -8 }{ 64 } } + { \left( \frac{ 1 }{ 3 } \right) }^{ 3 }$$

Evaluate

$$\frac{409}{108}\approx 3.787037037$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$\frac{9}{2}-\sqrt[4]{\frac{1}{256}}+\sqrt[3]{\frac{-8}{64}}+\left(\frac{1}{3}\right)^{3}$$

Calculate \sqrt[4]{\frac{1}{256}} and get \frac{1}{4}.

$$\frac{9}{2}-\frac{1}{4}+\sqrt[3]{\frac{-8}{64}}+\left(\frac{1}{3}\right)^{3}$$

Subtract \frac{1}{4} from \frac{9}{2} to get \frac{17}{4}.

$$\frac{17}{4}+\sqrt[3]{\frac{-8}{64}}+\left(\frac{1}{3}\right)^{3}$$

Reduce the fraction \frac{-8}{64} to lowest terms by extracting and canceling out 8.

$$\frac{17}{4}+\sqrt[3]{-\frac{1}{8}}+\left(\frac{1}{3}\right)^{3}$$

Calculate \sqrt[3]{-\frac{1}{8}} and get -\frac{1}{2}.

$$\frac{17}{4}-\frac{1}{2}+\left(\frac{1}{3}\right)^{3}$$

Subtract \frac{1}{2} from \frac{17}{4} to get \frac{15}{4}.

$$\frac{15}{4}+\left(\frac{1}{3}\right)^{3}$$

Calculate \frac{1}{3} to the power of 3 and get \frac{1}{27}.

$$\frac{15}{4}+\frac{1}{27}$$

Add \frac{15}{4} and \frac{1}{27} to get \frac{409}{108}.

$$\frac{409}{108}$$

Factor

$$\frac{409}{2 ^ {2} \cdot 3 ^ {3}} = 3\frac{85}{108} = 3.787037037037037$$