Solve [(2/5-1/3)^2(-3/5)]divsqrt{25/16}

$$[ ( \frac { 2 } { 5 } - \frac { 1 } { 3 } ) ^ { 2 } ( \frac { - 3 } { 5 } ) ] \div \sqrt { \frac { 25 } { 16 } }$$

Evaluate

$$-\frac{4}{1875}\approx -0.002133333$$

Solution Steps

Subtract \frac{1}{3} from \frac{2}{5} to get \frac{1}{15}.

$$\frac{\left(\frac{1}{15}\right)^{2}\times \frac{-3}{5}}{\sqrt{\frac{25}{16}}}$$

Calculate \frac{1}{15} to the power of 2 and get \frac{1}{225}.

$$\frac{\frac{1}{225}\times \frac{-3}{5}}{\sqrt{\frac{25}{16}}}$$

Fraction \frac{-3}{5} can be rewritten as -\frac{3}{5} by extracting the negative sign.

$$\frac{\frac{1}{225}\left(-\frac{3}{5}\right)}{\sqrt{\frac{25}{16}}}$$

Multiply \frac{1}{225} and -\frac{3}{5} to get -\frac{1}{375}.

$$\frac{-\frac{1}{375}}{\sqrt{\frac{25}{16}}}$$

Rewrite the square root of the division \frac{25}{16} as the division of square roots \frac{\sqrt{25}}{\sqrt{16}}. Take the square root of both numerator and denominator.

$$\frac{-\frac{1}{375}}{\frac{5}{4}}$$

Divide -\frac{1}{375} by \frac{5}{4} by multiplying -\frac{1}{375} by the reciprocal of \frac{5}{4}.

$$-\frac{1}{375}\times \frac{4}{5}$$

Multiply -\frac{1}{375} and \frac{4}{5} to get -\frac{4}{1875}.

$$-\frac{4}{1875}$$

Factor

$$-\frac{4}{1875} = -0.0021333333333333334$$