Solve [(3/5xy)^2:(3/5x)]^3:(3/5x)^2}:(3/5y^2)

$$[ ( \frac { 3 } { 5 } x y ) ^ { 2 } : ( \frac { 3 } { 5 } x ) ] ^ { 3 } : ( \frac { 3 } { 5 } x ) ^ { 2 } \} : ( \frac { 3 } { 5 } y ^ { 2 } )$$

Evaluate

$$\frac{3xy^{6}}{5}$$

Solution Steps

Expand \left(\frac{3}{5}xy\right)^{2}.

$$\frac{\left(\frac{\left(\frac{3}{5}\right)^{2}x^{2}y^{2}}{\frac{3}{5}x}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

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

$$\frac{\left(\frac{\frac{9}{25}x^{2}y^{2}}{\frac{3}{5}x}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Cancel out x in both numerator and denominator.

$$\frac{\left(\frac{\frac{9}{25}xy^{2}}{\frac{3}{5}}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Divide \frac{9}{25}xy^{2} by \frac{3}{5} by multiplying \frac{9}{25}xy^{2} by the reciprocal of \frac{3}{5}.

$$\frac{\left(\frac{\frac{9}{25}xy^{2}\times 5}{3}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Multiply \frac{9}{25} and 5 to get \frac{9}{5}.

$$\frac{\left(\frac{\frac{9}{5}xy^{2}}{3}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Divide \frac{9}{5}xy^{2} by 3 to get \frac{3}{5}xy^{2}.

$$\frac{\left(\frac{3}{5}xy^{2}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Expand \left(\frac{3}{5}xy^{2}\right)^{3}.

$$\frac{\left(\frac{3}{5}\right)^{3}x^{3}\left(y^{2}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\left(\frac{3}{5}\right)^{3}x^{3}y^{6}}{\left(\frac{3}{5}x\right)^{2}}$$

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

$$\frac{\frac{27}{125}x^{3}y^{6}}{\left(\frac{3}{5}x\right)^{2}}$$

Expand \left(\frac{3}{5}x\right)^{2}.

$$\frac{\frac{27}{125}x^{3}y^{6}}{\left(\frac{3}{5}\right)^{2}x^{2}}$$

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

$$\frac{\frac{27}{125}x^{3}y^{6}}{\frac{9}{25}x^{2}}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{\frac{27}{125}xy^{6}}{\frac{9}{25}}$$

Divide \frac{27}{125}xy^{6} by \frac{9}{25} by multiplying \frac{27}{125}xy^{6} by the reciprocal of \frac{9}{25}.

$$\frac{\frac{27}{125}xy^{6}\times 25}{9}$$

Multiply \frac{27}{125} and 25 to get \frac{27}{5}.

$$\frac{\frac{27}{5}xy^{6}}{9}$$

Divide \frac{27}{5}xy^{6} by 9 to get \frac{3}{5}xy^{6}.

$$\frac{3}{5}xy^{6}$$

Expand

$$\frac{3xy^{6}}{5}$$

Solution Steps

Expand \left(\frac{3}{5}xy\right)^{2}.

$$\frac{\left(\frac{\left(\frac{3}{5}\right)^{2}x^{2}y^{2}}{\frac{3}{5}x}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

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

$$\frac{\left(\frac{\frac{9}{25}x^{2}y^{2}}{\frac{3}{5}x}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Cancel out x in both numerator and denominator.

$$\frac{\left(\frac{\frac{9}{25}xy^{2}}{\frac{3}{5}}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Divide \frac{9}{25}xy^{2} by \frac{3}{5} by multiplying \frac{9}{25}xy^{2} by the reciprocal of \frac{3}{5}.

$$\frac{\left(\frac{\frac{9}{25}xy^{2}\times 5}{3}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Multiply \frac{9}{25} and 5 to get \frac{9}{5}.

$$\frac{\left(\frac{\frac{9}{5}xy^{2}}{3}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Divide \frac{9}{5}xy^{2} by 3 to get \frac{3}{5}xy^{2}.

$$\frac{\left(\frac{3}{5}xy^{2}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

Expand \left(\frac{3}{5}xy^{2}\right)^{3}.

$$\frac{\left(\frac{3}{5}\right)^{3}x^{3}\left(y^{2}\right)^{3}}{\left(\frac{3}{5}x\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\left(\frac{3}{5}\right)^{3}x^{3}y^{6}}{\left(\frac{3}{5}x\right)^{2}}$$

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

$$\frac{\frac{27}{125}x^{3}y^{6}}{\left(\frac{3}{5}x\right)^{2}}$$

Expand \left(\frac{3}{5}x\right)^{2}.

$$\frac{\frac{27}{125}x^{3}y^{6}}{\left(\frac{3}{5}\right)^{2}x^{2}}$$

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

$$\frac{\frac{27}{125}x^{3}y^{6}}{\frac{9}{25}x^{2}}$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{\frac{27}{125}xy^{6}}{\frac{9}{25}}$$

Divide \frac{27}{125}xy^{6} by \frac{9}{25} by multiplying \frac{27}{125}xy^{6} by the reciprocal of \frac{9}{25}.

$$\frac{\frac{27}{125}xy^{6}\times 25}{9}$$

Multiply \frac{27}{125} and 25 to get \frac{27}{5}.

$$\frac{\frac{27}{5}xy^{6}}{9}$$

Divide \frac{27}{5}xy^{6} by 9 to get \frac{3}{5}xy^{6}.

$$\frac{3}{5}xy^{6}$$