(5÷3)^-1-(5÷2) ÷(3÷10)^-3 solve with steps
You asked:
Evaluate the expression: \({\left( \frac{5}{3} \right)}^{-1} - \frac{\frac{5}{2}}{{\left( \frac{3}{10} \right)}^{-3}}\)
MathBot Answer:
\[{\left( \frac{5}{3} \right)}^{-1} - \frac{\frac{5}{2}}{{\left( \frac{3}{10} \right)}^{-3}} = \frac{213}{400} = 0.5325\]
\[\begin{aligned}{\left( \frac{5}{3} \right)}^{-1} - \frac{\frac{5}{2}}{{\left( \frac{3}{10} \right)}^{-3}}& = \frac{1}{\frac{5}{3}} - \frac{5}{2} \cdot \frac{1}{\frac{1}{\left(\frac{3}{10}\right)^{3}}}\\& = \frac{3}{5} - \frac{5}{2} \cdot \frac{1}{\frac{1}{\left(\frac{3}{10}\right)^{3}}}\\& = \frac{3}{5} - \frac{5}{2} \cdot \frac{1}{\frac{1000}{27}}\\& = \frac{3}{5} - \frac{27}{400}\\& = \frac{213}{400}\end{aligned}\]