Solve (-3x^{3}y^{4})^3div(5x^3y^6)^2

$$( - 3 x ^ { 3 } y ^ { 4 } ) ^ { 3 } \div ( 5 x ^ { 3 } y ^ { 6 } ) ^ { 2 }$$

Evaluate

$$-\frac{27x^{3}}{25}$$

Solution Steps

Expand \left(-3x^{3}y^{4}\right)^{3}.

$$\frac{\left(-3\right)^{3}\left(x^{3}\right)^{3}\left(y^{4}\right)^{3}}{\left(5x^{3}y^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{\left(-3\right)^{3}x^{9}\left(y^{4}\right)^{3}}{\left(5x^{3}y^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{\left(-3\right)^{3}x^{9}y^{12}}{\left(5x^{3}y^{6}\right)^{2}}$$

Calculate -3 to the power of 3 and get -27.

$$\frac{-27x^{9}y^{12}}{\left(5x^{3}y^{6}\right)^{2}}$$

Expand \left(5x^{3}y^{6}\right)^{2}.

$$\frac{-27x^{9}y^{12}}{5^{2}\left(x^{3}\right)^{2}\left(y^{6}\right)^{2}}$$

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

$$\frac{-27x^{9}y^{12}}{5^{2}x^{6}\left(y^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{-27x^{9}y^{12}}{5^{2}x^{6}y^{12}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{-27x^{9}y^{12}}{25x^{6}y^{12}}$$

Cancel out x^{6}y^{12} in both numerator and denominator.

$$\frac{-27x^{3}}{25}$$

Expand

$$-\frac{27x^{3}}{25}$$

Solution Steps

Expand \left(-3x^{3}y^{4}\right)^{3}.

$$\frac{\left(-3\right)^{3}\left(x^{3}\right)^{3}\left(y^{4}\right)^{3}}{\left(5x^{3}y^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{\left(-3\right)^{3}x^{9}\left(y^{4}\right)^{3}}{\left(5x^{3}y^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{\left(-3\right)^{3}x^{9}y^{12}}{\left(5x^{3}y^{6}\right)^{2}}$$

Calculate -3 to the power of 3 and get -27.

$$\frac{-27x^{9}y^{12}}{\left(5x^{3}y^{6}\right)^{2}}$$

Expand \left(5x^{3}y^{6}\right)^{2}.

$$\frac{-27x^{9}y^{12}}{5^{2}\left(x^{3}\right)^{2}\left(y^{6}\right)^{2}}$$

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

$$\frac{-27x^{9}y^{12}}{5^{2}x^{6}\left(y^{6}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{-27x^{9}y^{12}}{5^{2}x^{6}y^{12}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{-27x^{9}y^{12}}{25x^{6}y^{12}}$$

Cancel out x^{6}y^{12} in both numerator and denominator.

$$\frac{-27x^{3}}{25}$$