Solve (19/16)^frac{1{2}}-(-1/2)^-2+(210/27)^frac{1{3}}+3.14^0

$$( 1 \frac { 9 } { 16 } ) ^ { \frac { 1 } { 2 } } - ( - \frac { 1 } { 2 } ) ^ { - 2 } + ( 2 \frac { 10 } { 27 } ) ^ { \frac { 1 } { 3 } } + 3.14 ^ { 0 }$$

Evaluate

$$-\frac{5}{12}\approx -0.416666667$$

Solution Steps

Multiply 1 and 16 to get 16.

$$\left(\frac{16+9}{16}\right)^{\frac{1}{2}}-\left(-\frac{1}{2}\right)^{-2}+\left(\frac{2\times 27+10}{27}\right)^{\frac{1}{3}}+3.14^{0}$$

Add 16 and 9 to get 25.

$$\left(\frac{25}{16}\right)^{\frac{1}{2}}-\left(-\frac{1}{2}\right)^{-2}+\left(\frac{2\times 27+10}{27}\right)^{\frac{1}{3}}+3.14^{0}$$

Calculate \frac{25}{16} to the power of \frac{1}{2} and get \frac{5}{4}.

$$\frac{5}{4}-\left(-\frac{1}{2}\right)^{-2}+\left(\frac{2\times 27+10}{27}\right)^{\frac{1}{3}}+3.14^{0}$$

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

$$\frac{5}{4}-4+\left(\frac{2\times 27+10}{27}\right)^{\frac{1}{3}}+3.14^{0}$$

Subtract 4 from \frac{5}{4} to get -\frac{11}{4}.

$$-\frac{11}{4}+\left(\frac{2\times 27+10}{27}\right)^{\frac{1}{3}}+3.14^{0}$$

Multiply 2 and 27 to get 54.

$$-\frac{11}{4}+\left(\frac{54+10}{27}\right)^{\frac{1}{3}}+3.14^{0}$$

Add 54 and 10 to get 64.

$$-\frac{11}{4}+\left(\frac{64}{27}\right)^{\frac{1}{3}}+3.14^{0}$$

Calculate \frac{64}{27} to the power of \frac{1}{3} and get \frac{4}{3}.

$$-\frac{11}{4}+\frac{4}{3}+3.14^{0}$$

Add -\frac{11}{4} and \frac{4}{3} to get -\frac{17}{12}.

$$-\frac{17}{12}+3.14^{0}$$

Calculate 3.14 to the power of 0 and get 1.

$$-\frac{17}{12}+1$$

Add -\frac{17}{12} and 1 to get -\frac{5}{12}.

$$-\frac{5}{12}$$

Factor

$$-\frac{5}{12} = -0.4166666666666667$$