Solve frac{(-4x^{3}y^{3})^6}{(8x^5y^8)^3}

$$\frac { ( - 4 x ^ { 3 } y ^ { 3 } ) ^ { 6 } } { ( 8 x ^ { 5 } y ^ { 8 } ) ^ { 3 } }$$

Evaluate

$$\frac{8x^{3}}{y^{6}}$$

Solution Steps

Expand \left(-4x^{3}y^{3}\right)^{6}.

$$\frac{\left(-4\right)^{6}\left(x^{3}\right)^{6}\left(y^{3}\right)^{6}}{\left(8x^{5}y^{8}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 6 to get 18.

$$\frac{\left(-4\right)^{6}x^{18}\left(y^{3}\right)^{6}}{\left(8x^{5}y^{8}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 6 to get 18.

$$\frac{\left(-4\right)^{6}x^{18}y^{18}}{\left(8x^{5}y^{8}\right)^{3}}$$

Calculate -4 to the power of 6 and get 4096.

$$\frac{4096x^{18}y^{18}}{\left(8x^{5}y^{8}\right)^{3}}$$

Expand \left(8x^{5}y^{8}\right)^{3}.

$$\frac{4096x^{18}y^{18}}{8^{3}\left(x^{5}\right)^{3}\left(y^{8}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{4096x^{18}y^{18}}{8^{3}x^{15}\left(y^{8}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$\frac{4096x^{18}y^{18}}{8^{3}x^{15}y^{24}}$$

Calculate 8 to the power of 3 and get 512.

$$\frac{4096x^{18}y^{18}}{512x^{15}y^{24}}$$

Cancel out 512x^{15}y^{18} in both numerator and denominator.

$$\frac{8x^{3}}{y^{6}}$$

Expand

$$\frac{8x^{3}}{y^{6}}$$

Solution Steps

Expand \left(-4x^{3}y^{3}\right)^{6}.

$$\frac{\left(-4\right)^{6}\left(x^{3}\right)^{6}\left(y^{3}\right)^{6}}{\left(8x^{5}y^{8}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 6 to get 18.

$$\frac{\left(-4\right)^{6}x^{18}\left(y^{3}\right)^{6}}{\left(8x^{5}y^{8}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 6 to get 18.

$$\frac{\left(-4\right)^{6}x^{18}y^{18}}{\left(8x^{5}y^{8}\right)^{3}}$$

Calculate -4 to the power of 6 and get 4096.

$$\frac{4096x^{18}y^{18}}{\left(8x^{5}y^{8}\right)^{3}}$$

Expand \left(8x^{5}y^{8}\right)^{3}.

$$\frac{4096x^{18}y^{18}}{8^{3}\left(x^{5}\right)^{3}\left(y^{8}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{4096x^{18}y^{18}}{8^{3}x^{15}\left(y^{8}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$\frac{4096x^{18}y^{18}}{8^{3}x^{15}y^{24}}$$

Calculate 8 to the power of 3 and get 512.

$$\frac{4096x^{18}y^{18}}{512x^{15}y^{24}}$$

Cancel out 512x^{15}y^{18} in both numerator and denominator.

$$\frac{8x^{3}}{y^{6}}$$