Solve [(3/5)^2:27/25]:1/6=

$$[ ( \frac { 3 } { 5 } ) ^ { 2 } : \frac { 27 } { 25 } ] : \frac { 1 } { 6 } =$$

Evaluate

$$2$$

Solution Steps

Divide \frac{\left(\frac{3}{5}\right)^{2}}{\frac{27}{25}} by \frac{1}{6} by multiplying \frac{\left(\frac{3}{5}\right)^{2}}{\frac{27}{25}} by the reciprocal of \frac{1}{6}.

$$\frac{\left(\frac{3}{5}\right)^{2}\times 6}{\frac{27}{25}}$$

Calculate \frac{3}{5} to the power of 2 and get \frac{9}{25}.

$$\frac{\frac{9}{25}\times 6}{\frac{27}{25}}$$

Express \frac{9}{25}\times 6 as a single fraction.

$$\frac{\frac{9\times 6}{25}}{\frac{27}{25}}$$

Multiply 9 and 6 to get 54.

$$\frac{\frac{54}{25}}{\frac{27}{25}}$$

Divide \frac{54}{25} by \frac{27}{25} by multiplying \frac{54}{25} by the reciprocal of \frac{27}{25}.

$$\frac{54}{25}\times \frac{25}{27}$$

Multiply \frac{54}{25} times \frac{25}{27} by multiplying numerator times numerator and denominator times denominator.

$$\frac{54\times 25}{25\times 27}$$

Cancel out 25 in both numerator and denominator.

$$\frac{54}{27}$$

Divide 54 by 27 to get 2.

$$2$$

Factor

$$2$$