Solve (sqrt[4]{(1^-1/5)+2^-4})-(4/5)+(3^2*1/20)

$$( \sqrt[ 4 ]{ ( \frac{ { 1 }^{ -1 } }{ 5 } )+ { 2 }^{ -4 } } )-( \frac{ 4 }{ 5 } )+( { 3 }^{ 2 } \times \frac{ 1 }{ 20 } )$$

Evaluate

$$\frac{5^{\frac{3}{4}}\sqrt[4]{21}}{10}-\frac{7}{20}\approx 0.365784561$$

Solution Steps

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

$$\sqrt[4]{\frac{1}{5}+2^{-4}}-\frac{4}{5}+3^{2}\times \frac{1}{20}$$

Calculate 2 to the power of -4 and get \frac{1}{16}.

$$\sqrt[4]{\frac{1}{5}+\frac{1}{16}}-\frac{4}{5}+3^{2}\times \frac{1}{20}$$

Add \frac{1}{5} and \frac{1}{16} to get \frac{21}{80}.

$$\sqrt[4]{\frac{21}{80}}-\frac{4}{5}+3^{2}\times \frac{1}{20}$$

Calculate 3 to the power of 2 and get 9.

$$\sqrt[4]{\frac{21}{80}}-\frac{4}{5}+9\times \frac{1}{20}$$

Multiply 9 and \frac{1}{20} to get \frac{9}{20}.

$$\sqrt[4]{\frac{21}{80}}-\frac{4}{5}+\frac{9}{20}$$

Add -\frac{4}{5} and \frac{9}{20} to get -\frac{7}{20}.

$$\sqrt[4]{\frac{21}{80}}-\frac{7}{20}$$

Factor

$$\frac{2 \cdot 5 ^ {\frac{3}{4}} \sqrt[4]{21} - 7}{20} = 0.36578456137163223$$