Solve 2^-1+(2/3)^-2+(19/4)^0+1/5^-1

$$2 ^ { - 1 } + ( \frac { 2 } { 3 } ) ^ { - 2 } + ( \frac { 19 } { 4 } ) ^ { 0 } + \frac { 1 } { 5 ^ { - 1 } }$$

Evaluate

$$\frac{35}{4}=8.75$$

Solution Steps

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

$$\frac{1}{2}+\left(\frac{2}{3}\right)^{-2}+\left(\frac{19}{4}\right)^{0}+\frac{1}{5^{-1}}$$

Calculate \frac{2}{3} to the power of -2 and get \frac{9}{4}.

$$\frac{1}{2}+\frac{9}{4}+\left(\frac{19}{4}\right)^{0}+\frac{1}{5^{-1}}$$

Add \frac{1}{2} and \frac{9}{4} to get \frac{11}{4}.

$$\frac{11}{4}+\left(\frac{19}{4}\right)^{0}+\frac{1}{5^{-1}}$$

Calculate \frac{19}{4} to the power of 0 and get 1.

$$\frac{11}{4}+1+\frac{1}{5^{-1}}$$

Add \frac{11}{4} and 1 to get \frac{15}{4}.

$$\frac{15}{4}+\frac{1}{5^{-1}}$$

Calculate 5 to the power of -1 and get \frac{1}{5}.

$$\frac{15}{4}+\frac{1}{\frac{1}{5}}$$

Divide 1 by \frac{1}{5} by multiplying 1 by the reciprocal of \frac{1}{5}.

$$\frac{15}{4}+1\times 5$$

Multiply 1 and 5 to get 5.

$$\frac{15}{4}+5$$

Add \frac{15}{4} and 5 to get \frac{35}{4}.

$$\frac{35}{4}$$

Factor

$$\frac{5 \cdot 7}{2 ^ {2}} = 8\frac{3}{4} = 8.75$$