Solve {left(8x^18y^7/16x^8y^11right)}^4

$${ \left( \frac{ 8 { x }^{ 18 } { y }^{ 7 } }{ 16 { x }^{ 8 } { y }^{ 11 } } \right) }^{ 4 }$$

Evaluate

$$\frac{x^{40}}{16y^{16}}$$

Solution Steps

Cancel out 8y^{7}x^{8} in both numerator and denominator.

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

To raise \frac{x^{10}}{2y^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply 10 and 4 to get 40.

$$\frac{x^{40}}{\left(2y^{4}\right)^{4}}$$

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

$$\frac{x^{40}}{2^{4}\left(y^{4}\right)^{4}}$$

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

$$\frac{x^{40}}{2^{4}y^{16}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{x^{40}}{16y^{16}}$$

Expand

$$\frac{x^{40}}{16y^{16}}$$

Solution Steps

Cancel out 8y^{7}x^{8} in both numerator and denominator.

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

To raise \frac{x^{10}}{2y^{4}} to a power, raise both numerator and denominator to the power and then divide.

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

To raise a power to another power, multiply the exponents. Multiply 10 and 4 to get 40.

$$\frac{x^{40}}{\left(2y^{4}\right)^{4}}$$

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

$$\frac{x^{40}}{2^{4}\left(y^{4}\right)^{4}}$$

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

$$\frac{x^{40}}{2^{4}y^{16}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{x^{40}}{16y^{16}}$$