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

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

Evaluate

$$\frac{9x^{9}}{8y^{2}}$$

Solution Steps

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

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

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

$$\frac{\left(-3\right)^{2}x^{12}\left(y^{5}\right)^{2}}{\left(2xy^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{\left(-3\right)^{2}x^{12}y^{10}}{\left(2xy^{4}\right)^{3}}$$

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

$$\frac{9x^{12}y^{10}}{\left(2xy^{4}\right)^{3}}$$

Expand \left(2xy^{4}\right)^{3}.

$$\frac{9x^{12}y^{10}}{2^{3}x^{3}\left(y^{4}\right)^{3}}$$

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

$$\frac{9x^{12}y^{10}}{2^{3}x^{3}y^{12}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{9x^{12}y^{10}}{8x^{3}y^{12}}$$

Cancel out x^{3}y^{10} in both numerator and denominator.

$$\frac{9x^{9}}{8y^{2}}$$

Expand

$$\frac{9x^{9}}{8y^{2}}$$

Solution Steps

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

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

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

$$\frac{\left(-3\right)^{2}x^{12}\left(y^{5}\right)^{2}}{\left(2xy^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{\left(-3\right)^{2}x^{12}y^{10}}{\left(2xy^{4}\right)^{3}}$$

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

$$\frac{9x^{12}y^{10}}{\left(2xy^{4}\right)^{3}}$$

Expand \left(2xy^{4}\right)^{3}.

$$\frac{9x^{12}y^{10}}{2^{3}x^{3}\left(y^{4}\right)^{3}}$$

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

$$\frac{9x^{12}y^{10}}{2^{3}x^{3}y^{12}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{9x^{12}y^{10}}{8x^{3}y^{12}}$$

Cancel out x^{3}y^{10} in both numerator and denominator.

$$\frac{9x^{9}}{8y^{2}}$$