Solve left(4x^y^2zright)^4/{left(-2x^2y{z^5right)}^4}

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

Evaluate

$$\frac{16\times \left(\frac{y}{x}\right)^{4}}{z^{16}}$$

Solution Steps

Calculate x to the power of 1 and get x.

$$\frac{\left(4xy^{2}z\right)^{4}}{\left(-2x^{2}yz^{5}\right)^{4}}$$

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{4^{4}x^{4}y^{8}z^{4}}{\left(-2x^{2}yz^{5}\right)^{4}}$$

Calculate 4 to the power of 4 and get 256.

$$\frac{256x^{4}y^{8}z^{4}}{\left(-2x^{2}yz^{5}\right)^{4}}$$

Expand \left(-2x^{2}yz^{5}\right)^{4}.

$$\frac{256x^{4}y^{8}z^{4}}{\left(-2\right)^{4}\left(x^{2}\right)^{4}y^{4}\left(z^{5}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{256x^{4}y^{8}z^{4}}{\left(-2\right)^{4}x^{8}y^{4}\left(z^{5}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$\frac{256x^{4}y^{8}z^{4}}{\left(-2\right)^{4}x^{8}y^{4}z^{20}}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{256x^{4}y^{8}z^{4}}{16x^{8}y^{4}z^{20}}$$

Cancel out 16x^{4}y^{4}z^{4} in both numerator and denominator.

$$\frac{16y^{4}}{x^{4}z^{16}}$$

Expand

$$\frac{16\times \left(\frac{y}{x}\right)^{4}}{z^{16}}$$

Solution Steps

Calculate x to the power of 1 and get x.

$$\frac{\left(4xy^{2}z\right)^{4}}{\left(-2x^{2}yz^{5}\right)^{4}}$$

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

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

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{4^{4}x^{4}y^{8}z^{4}}{\left(-2x^{2}yz^{5}\right)^{4}}$$

Calculate 4 to the power of 4 and get 256.

$$\frac{256x^{4}y^{8}z^{4}}{\left(-2x^{2}yz^{5}\right)^{4}}$$

Expand \left(-2x^{2}yz^{5}\right)^{4}.

$$\frac{256x^{4}y^{8}z^{4}}{\left(-2\right)^{4}\left(x^{2}\right)^{4}y^{4}\left(z^{5}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{256x^{4}y^{8}z^{4}}{\left(-2\right)^{4}x^{8}y^{4}\left(z^{5}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$\frac{256x^{4}y^{8}z^{4}}{\left(-2\right)^{4}x^{8}y^{4}z^{20}}$$

Calculate -2 to the power of 4 and get 16.

$$\frac{256x^{4}y^{8}z^{4}}{16x^{8}y^{4}z^{20}}$$

Cancel out 16x^{4}y^{4}z^{4} in both numerator and denominator.

$$\frac{16y^{4}}{x^{4}z^{16}}$$