Solve frac{(4xy^{2}z)^4}{(-2x^2yz^3)^3}

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

Evaluate

$$-\frac{32\times \left(\frac{y}{z}\right)^{5}}{x^{2}}$$

Solution Steps

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

$$\frac{4^{4}x^{4}\left(y^{2}\right)^{4}z^{4}}{\left(-2x^{2}yz^{3}\right)^{3}}$$

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

$$\frac{4^{4}x^{4}y^{8}z^{4}}{\left(-2x^{2}yz^{3}\right)^{3}}$$

Calculate 4 to the power of 4 and get 256.

$$\frac{256x^{4}y^{8}z^{4}}{\left(-2x^{2}yz^{3}\right)^{3}}$$

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

$$\frac{256x^{4}y^{8}z^{4}}{\left(-2\right)^{3}\left(x^{2}\right)^{3}y^{3}\left(z^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{256x^{4}y^{8}z^{4}}{\left(-2\right)^{3}x^{6}y^{3}\left(z^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{256x^{4}y^{8}z^{4}}{\left(-2\right)^{3}x^{6}y^{3}z^{9}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{256x^{4}y^{8}z^{4}}{-8x^{6}y^{3}z^{9}}$$

Cancel out 8y^{3}x^{4}z^{4} in both numerator and denominator.

$$\frac{32y^{5}}{-x^{2}z^{5}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{-32y^{5}}{x^{2}z^{5}}$$

Expand

$$-\frac{32\times \left(\frac{y}{z}\right)^{5}}{x^{2}}$$

Solution Steps

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

$$\frac{4^{4}x^{4}\left(y^{2}\right)^{4}z^{4}}{\left(-2x^{2}yz^{3}\right)^{3}}$$

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

$$\frac{4^{4}x^{4}y^{8}z^{4}}{\left(-2x^{2}yz^{3}\right)^{3}}$$

Calculate 4 to the power of 4 and get 256.

$$\frac{256x^{4}y^{8}z^{4}}{\left(-2x^{2}yz^{3}\right)^{3}}$$

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

$$\frac{256x^{4}y^{8}z^{4}}{\left(-2\right)^{3}\left(x^{2}\right)^{3}y^{3}\left(z^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{256x^{4}y^{8}z^{4}}{\left(-2\right)^{3}x^{6}y^{3}\left(z^{3}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{256x^{4}y^{8}z^{4}}{\left(-2\right)^{3}x^{6}y^{3}z^{9}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{256x^{4}y^{8}z^{4}}{-8x^{6}y^{3}z^{9}}$$

Cancel out 8y^{3}x^{4}z^{4} in both numerator and denominator.

$$\frac{32y^{5}}{-x^{2}z^{5}}$$

Cancel out -1 in both numerator and denominator.

$$\frac{-32y^{5}}{x^{2}z^{5}}$$