Solve (-3)^2[-6^2*(1/6)^2-4/5]div(-52/5)

$$( - 3 ) ^ { 2 } [ - 6 ^ { 2 } \times ( \frac { 1 } { 6 } ) ^ { 2 } - \frac { 4 } { 5 } ] \div ( - 5 \frac { 2 } { 5 } )$$

Evaluate

$$3$$

Solution Steps

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

$$\frac{9\left(\left(-6^{2}\right)\times \left(\frac{1}{6}\right)^{2}-\frac{4}{5}\right)}{-\frac{5\times 5+2}{5}}$$

Calculate 6 to the power of 2 and get 36.

$$\frac{9\left(-36\times \left(\frac{1}{6}\right)^{2}-\frac{4}{5}\right)}{-\frac{5\times 5+2}{5}}$$

Calculate \frac{1}{6} to the power of 2 and get \frac{1}{36}.

$$\frac{9\left(-36\times \frac{1}{36}-\frac{4}{5}\right)}{-\frac{5\times 5+2}{5}}$$

Multiply -36 times \frac{1}{36}.

$$\frac{9\left(-1-\frac{4}{5}\right)}{-\frac{5\times 5+2}{5}}$$

Convert -1 to fraction -\frac{5}{5}.

$$\frac{9\left(-\frac{5}{5}-\frac{4}{5}\right)}{-\frac{5\times 5+2}{5}}$$

Since -\frac{5}{5} and \frac{4}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{9\times \frac{-5-4}{5}}{-\frac{5\times 5+2}{5}}$$

Subtract 4 from -5 to get -9.

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

Express 9\left(-\frac{9}{5}\right) as a single fraction.

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

Multiply 9 and -9 to get -81.

$$\frac{\frac{-81}{5}}{-\frac{5\times 5+2}{5}}$$

Fraction \frac{-81}{5} can be rewritten as -\frac{81}{5} by extracting the negative sign.

$$\frac{-\frac{81}{5}}{-\frac{5\times 5+2}{5}}$$

Multiply 5 and 5 to get 25.

$$\frac{-\frac{81}{5}}{-\frac{25+2}{5}}$$

Add 25 and 2 to get 27.

$$\frac{-\frac{81}{5}}{-\frac{27}{5}}$$

Divide -\frac{81}{5} by -\frac{27}{5} by multiplying -\frac{81}{5} by the reciprocal of -\frac{27}{5}.

$$-\frac{81}{5}\left(-\frac{5}{27}\right)$$

Multiply -\frac{81}{5} times -\frac{5}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-81\left(-5\right)}{5\times 27}$$

Do the multiplications in the fraction \frac{-81\left(-5\right)}{5\times 27}.

$$\frac{405}{135}$$

Divide 405 by 135 to get 3.

$$3$$

Factor

$$3$$