Solve (-3x^2y^4)div(3/5y^2)^2

$$( - 3 x ^ { 2 } y ^ { 4 } ) \div ( \frac { 3 } { 5 } y ^ { 2 } ) ^ { 2 }$$

Evaluate

$$-\frac{25x^{2}}{3}$$

Solution Steps

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

$$\frac{-3x^{2}y^{4}}{\left(\frac{3}{5}\right)^{2}\left(y^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{-3x^{2}y^{4}}{\left(\frac{3}{5}\right)^{2}y^{4}}$$

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

$$\frac{-3x^{2}y^{4}}{\frac{9}{25}y^{4}}$$

Cancel out y^{4} in both numerator and denominator.

$$\frac{-3x^{2}}{\frac{9}{25}}$$

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

$$\frac{-3x^{2}\times 25}{9}$$

Multiply -3 and 25 to get -75.

$$\frac{-75x^{2}}{9}$$

Divide -75x^{2} by 9 to get -\frac{25}{3}x^{2}.

$$-\frac{25}{3}x^{2}$$

Expand

$$-\frac{25x^{2}}{3}$$

Solution Steps

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

$$\frac{-3x^{2}y^{4}}{\left(\frac{3}{5}\right)^{2}\left(y^{2}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{-3x^{2}y^{4}}{\left(\frac{3}{5}\right)^{2}y^{4}}$$

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

$$\frac{-3x^{2}y^{4}}{\frac{9}{25}y^{4}}$$

Cancel out y^{4} in both numerator and denominator.

$$\frac{-3x^{2}}{\frac{9}{25}}$$

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

$$\frac{-3x^{2}\times 25}{9}$$

Multiply -3 and 25 to get -75.

$$\frac{-75x^{2}}{9}$$

Divide -75x^{2} by 9 to get -\frac{25}{3}x^{2}.

$$-\frac{25}{3}x^{2}$$