Solve (1/5)^-1*5^-2+sqrt{9/4}+4*(2/5)^-1=

$$( \frac { 1 } { 5 } ) ^ { - 1 } \cdot 5 ^ { - 2 } + \sqrt { \frac { 9 } { 4 } } + 4 \cdot ( \frac { 2 } { 5 } ) ^ { - 1 } =$$

Evaluate

$$\frac{117}{10}=11.7$$

Solution Steps

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

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

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

$$5\times \frac{1}{25}+\sqrt{\frac{9}{4}}+4\times \left(\frac{2}{5}\right)^{-1}$$

Multiply 5 and \frac{1}{25} to get \frac{1}{5}.

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

Rewrite the square root of the division \frac{9}{4} as the division of square roots \frac{\sqrt{9}}{\sqrt{4}}. Take the square root of both numerator and denominator.

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

Add \frac{1}{5} and \frac{3}{2} to get \frac{17}{10}.

$$\frac{17}{10}+4\times \left(\frac{2}{5}\right)^{-1}$$

Calculate \frac{2}{5} to the power of -1 and get \frac{5}{2}.

$$\frac{17}{10}+4\times \frac{5}{2}$$

Multiply 4 and \frac{5}{2} to get 10.

$$\frac{17}{10}+10$$

Add \frac{17}{10} and 10 to get \frac{117}{10}.

$$\frac{117}{10}$$

Factor

$$\frac{3 ^ {2} \cdot 13}{2 \cdot 5} = 11\frac{7}{10} = 11.7$$