Solve {left(frac{2x^4/yright)}^4}{{left(3x^2/y^3right)}^5}

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

Evaluate

$$\frac{16x^{6}y^{11}}{243}$$

Solution Steps

To raise \frac{2x^{4}}{y} to a power, raise both numerator and denominator to the power and then divide.

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

To raise \frac{3x^{2}}{y^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

Divide \frac{\left(2x^{4}\right)^{4}}{y^{4}} by \frac{\left(3x^{2}\right)^{5}}{\left(y^{3}\right)^{5}} by multiplying \frac{\left(2x^{4}\right)^{4}}{y^{4}} by the reciprocal of \frac{\left(3x^{2}\right)^{5}}{\left(y^{3}\right)^{5}}.

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

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

$$\frac{\left(2x^{4}\right)^{4}y^{15}}{y^{4}\times \left(3x^{2}\right)^{5}}$$

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

$$\frac{2^{4}\left(x^{4}\right)^{4}y^{15}}{y^{4}\times \left(3x^{2}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\frac{2^{4}x^{16}y^{15}}{y^{4}\times \left(3x^{2}\right)^{5}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16x^{16}y^{15}}{y^{4}\times \left(3x^{2}\right)^{5}}$$

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

$$\frac{16x^{16}y^{15}}{y^{4}\times 3^{5}\left(x^{2}\right)^{5}}$$

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

$$\frac{16x^{16}y^{15}}{y^{4}\times 3^{5}x^{10}}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{16x^{16}y^{15}}{y^{4}\times 243x^{10}}$$

Cancel out y^{4}x^{10} in both numerator and denominator.

$$\frac{16x^{6}y^{11}}{243}$$

Expand

$$\frac{16x^{6}y^{11}}{243}$$

Solution Steps

To raise \frac{2x^{4}}{y} to a power, raise both numerator and denominator to the power and then divide.

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

To raise \frac{3x^{2}}{y^{3}} to a power, raise both numerator and denominator to the power and then divide.

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

Divide \frac{\left(2x^{4}\right)^{4}}{y^{4}} by \frac{\left(3x^{2}\right)^{5}}{\left(y^{3}\right)^{5}} by multiplying \frac{\left(2x^{4}\right)^{4}}{y^{4}} by the reciprocal of \frac{\left(3x^{2}\right)^{5}}{\left(y^{3}\right)^{5}}.

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

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

$$\frac{\left(2x^{4}\right)^{4}y^{15}}{y^{4}\times \left(3x^{2}\right)^{5}}$$

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

$$\frac{2^{4}\left(x^{4}\right)^{4}y^{15}}{y^{4}\times \left(3x^{2}\right)^{5}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\frac{2^{4}x^{16}y^{15}}{y^{4}\times \left(3x^{2}\right)^{5}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{16x^{16}y^{15}}{y^{4}\times \left(3x^{2}\right)^{5}}$$

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

$$\frac{16x^{16}y^{15}}{y^{4}\times 3^{5}\left(x^{2}\right)^{5}}$$

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

$$\frac{16x^{16}y^{15}}{y^{4}\times 3^{5}x^{10}}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{16x^{16}y^{15}}{y^{4}\times 243x^{10}}$$

Cancel out y^{4}x^{10} in both numerator and denominator.

$$\frac{16x^{6}y^{11}}{243}$$