Solve 1/25-(3/5)(-9/25)/3+frac{2(frac{3}{5})^3}{27}

$$\frac { 1 } { 25 } - \frac { ( \frac { 3 } { 5 } ) ( \frac { - 9 } { 25 } ) } { 3 } + \frac { 2 ( \frac { 3 } { 5 } ) ^ { 3 } } { 27 }$$

Evaluate

$$\frac{16}{125}=0.128$$

Solution Steps

Fraction \frac{-9}{25} can be rewritten as -\frac{9}{25} by extracting the negative sign.

$$\frac{1}{25}-\frac{\frac{3}{5}\left(-\frac{9}{25}\right)}{3}+\frac{2\times \left(\frac{3}{5}\right)^{3}}{27}$$

Multiply \frac{3}{5} times -\frac{9}{25} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{25}-\frac{\frac{3\left(-9\right)}{5\times 25}}{3}+\frac{2\times \left(\frac{3}{5}\right)^{3}}{27}$$

Do the multiplications in the fraction \frac{3\left(-9\right)}{5\times 25}.

$$\frac{1}{25}-\frac{\frac{-27}{125}}{3}+\frac{2\times \left(\frac{3}{5}\right)^{3}}{27}$$

Fraction \frac{-27}{125} can be rewritten as -\frac{27}{125} by extracting the negative sign.

$$\frac{1}{25}-\frac{-\frac{27}{125}}{3}+\frac{2\times \left(\frac{3}{5}\right)^{3}}{27}$$

Express \frac{-\frac{27}{125}}{3} as a single fraction.

$$\frac{1}{25}-\frac{-27}{125\times 3}+\frac{2\times \left(\frac{3}{5}\right)^{3}}{27}$$

Multiply 125 and 3 to get 375.

$$\frac{1}{25}-\frac{-27}{375}+\frac{2\times \left(\frac{3}{5}\right)^{3}}{27}$$

Reduce the fraction \frac{-27}{375} to lowest terms by extracting and canceling out 3.

$$\frac{1}{25}-\left(-\frac{9}{125}\right)+\frac{2\times \left(\frac{3}{5}\right)^{3}}{27}$$

The opposite of -\frac{9}{125} is \frac{9}{125}.

$$\frac{1}{25}+\frac{9}{125}+\frac{2\times \left(\frac{3}{5}\right)^{3}}{27}$$

Least common multiple of 25 and 125 is 125. Convert \frac{1}{25} and \frac{9}{125} to fractions with denominator 125.

$$\frac{5}{125}+\frac{9}{125}+\frac{2\times \left(\frac{3}{5}\right)^{3}}{27}$$

Since \frac{5}{125} and \frac{9}{125} have the same denominator, add them by adding their numerators.

$$\frac{5+9}{125}+\frac{2\times \left(\frac{3}{5}\right)^{3}}{27}$$

Add 5 and 9 to get 14.

$$\frac{14}{125}+\frac{2\times \left(\frac{3}{5}\right)^{3}}{27}$$

Calculate \frac{3}{5} to the power of 3 and get \frac{27}{125}.

$$\frac{14}{125}+\frac{2\times \frac{27}{125}}{27}$$

Express 2\times \frac{27}{125} as a single fraction.

$$\frac{14}{125}+\frac{\frac{2\times 27}{125}}{27}$$

Multiply 2 and 27 to get 54.

$$\frac{14}{125}+\frac{\frac{54}{125}}{27}$$

Express \frac{\frac{54}{125}}{27} as a single fraction.

$$\frac{14}{125}+\frac{54}{125\times 27}$$

Multiply 125 and 27 to get 3375.

$$\frac{14}{125}+\frac{54}{3375}$$

Reduce the fraction \frac{54}{3375} to lowest terms by extracting and canceling out 27.

$$\frac{14}{125}+\frac{2}{125}$$

Since \frac{14}{125} and \frac{2}{125} have the same denominator, add them by adding their numerators.

$$\frac{14+2}{125}$$

Add 14 and 2 to get 16.

$$\frac{16}{125}$$

Factor

$$\frac{2 ^ {4}}{5 ^ {3}} = 0.128$$