Solve (5/3-6/4)^{-1})^{1/2}-(1/25)^{-frac{1}{2}}*frac{(frac{3}{10})^2}{(frac{1}{5}-frac{1}{2})^2}-(frac{7}{2})^2*2^3divfrac{1}{4}

$$( \frac { 5 } { 3 } - \frac { 6 } { 4 } ) ^ { - 1 } ) ^ { \frac { 1 } { 2 } } - ( \frac { 1 } { 25 } ) ^ { - \frac { 1 } { 2 } } \times \frac { ( \frac { 3 } { 10 } ) ^ { 2 } } { ( \frac { 1 } { 5 } - \frac { 1 } { 2 } ) ^ { 2 } } - ( \frac { 7 } { 2 } ) ^ { 2 } \times 2 ^ { 3 } \div \frac { 1 } { 4 }$$

Evaluate

$$6$$

Solution Steps

Reduce the fraction \frac{6}{4} to lowest terms by extracting and canceling out 2.

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

Subtract \frac{3}{2} from \frac{5}{3} to get \frac{1}{6}.

$$\left(\frac{1}{6}\right)^{-1}$$

Calculate \frac{1}{6} to the power of -1 and get 6.

$$6$$

Factor

$$2\times 3$$