Solve (19/16)^frac{1{2}}+0.1^-2-(-3.14)^0-(-8/27)^-frac{1{3}}

$$( 1 \frac { 9 } { 16 } ) ^ { \frac { 1 } { 2 } } + 0.1 ^ { - 2 } - ( - 3.14 ) ^ { 0 } - ( - \frac { 8 } { 27 } ) ^ { - \frac { 1 } { 3 } }$$

Evaluate

$$101.75$$

Solution Steps

Multiply 1 and 16 to get 16.

$$\left(\frac{16+9}{16}\right)^{\frac{1}{2}}+0.1^{-2}-\left(-3.14\right)^{0}-\left(-\frac{8}{27}\right)^{-\frac{1}{3}}$$

Add 16 and 9 to get 25.

$$\left(\frac{25}{16}\right)^{\frac{1}{2}}+0.1^{-2}-\left(-3.14\right)^{0}-\left(-\frac{8}{27}\right)^{-\frac{1}{3}}$$

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

$$\frac{5}{4}+0.1^{-2}-\left(-3.14\right)^{0}-\left(-\frac{8}{27}\right)^{-\frac{1}{3}}$$

Calculate 0.1 to the power of -2 and get 100.

$$\frac{5}{4}+100-\left(-3.14\right)^{0}-\left(-\frac{8}{27}\right)^{-\frac{1}{3}}$$

Add \frac{5}{4} and 100 to get \frac{405}{4}.

$$\frac{405}{4}-\left(-3.14\right)^{0}-\left(-\frac{8}{27}\right)^{-\frac{1}{3}}$$

Calculate -3.14 to the power of 0 and get 1.

$$\frac{405}{4}-1-\left(-\frac{8}{27}\right)^{-\frac{1}{3}}$$

Subtract 1 from \frac{405}{4} to get \frac{401}{4}.

$$\frac{401}{4}-\left(-\frac{8}{27}\right)^{-\frac{1}{3}}$$

Calculate -\frac{8}{27} to the power of -\frac{1}{3} and get -\frac{3}{2}.

$$\frac{401}{4}-\left(-\frac{3}{2}\right)$$

The opposite of -\frac{3}{2} is \frac{3}{2}.

$$\frac{401}{4}+\frac{3}{2}$$

Add \frac{401}{4} and \frac{3}{2} to get \frac{407}{4}.

$$\frac{407}{4}$$

Factor

$$\frac{11 \cdot 37}{2 ^ {2}} = 101\frac{3}{4} = 101.75$$