Solve -3^2div[(-1/3)^3*(-3)^2+13/5div(-2)^2]

$$- 3 ^ { 2 } \div [ ( - \frac { 1 } { 3 } ) ^ { 3 } \times ( - 3 ) ^ { 2 } + 1 \frac { 3 } { 5 } \div ( - 2 ) ^ { 2 } ]$$

Evaluate

$$-135$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

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

Calculate -\frac{1}{3} to the power of 3 and get -\frac{1}{27}.

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

Calculate -3 to the power of 2 and get 9.

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

Express -\frac{1}{27}\times 9 as a single fraction.

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

Reduce the fraction \frac{-9}{27} to lowest terms by extracting and canceling out 9.

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

Multiply 1 and 5 to get 5.

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

Add 5 and 3 to get 8.

$$\frac{-9}{-\frac{1}{3}+\frac{\frac{8}{5}}{\left(-2\right)^{2}}}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{-9}{-\frac{1}{3}+\frac{\frac{8}{5}}{4}}$$

Express \frac{\frac{8}{5}}{4} as a single fraction.

$$\frac{-9}{-\frac{1}{3}+\frac{8}{5\times 4}}$$

Multiply 5 and 4 to get 20.

$$\frac{-9}{-\frac{1}{3}+\frac{8}{20}}$$

Reduce the fraction \frac{8}{20} to lowest terms by extracting and canceling out 4.

$$\frac{-9}{-\frac{1}{3}+\frac{2}{5}}$$

Least common multiple of 3 and 5 is 15. Convert -\frac{1}{3} and \frac{2}{5} to fractions with denominator 15.

$$\frac{-9}{-\frac{5}{15}+\frac{6}{15}}$$

Since -\frac{5}{15} and \frac{6}{15} have the same denominator, add them by adding their numerators.

$$\frac{-9}{\frac{-5+6}{15}}$$

Add -5 and 6 to get 1.

$$\frac{-9}{\frac{1}{15}}$$

Divide -9 by \frac{1}{15} by multiplying -9 by the reciprocal of \frac{1}{15}.

$$-9\times 15$$

Multiply -9 and 15 to get -135.

$$-135$$

Factor

$$-135$$