Solve (-3x^2yz)^3div(-x^3yz)^2

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

Evaluate

$$-27yz$$

Solution Steps

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

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

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

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

Calculate -3 to the power of 3 and get -27.

$$\frac{-27x^{6}y^{3}z^{3}}{\left(\left(-x^{3}\right)yz\right)^{2}}$$

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

$$\frac{-27x^{6}y^{3}z^{3}}{\left(-x^{3}\right)^{2}y^{2}z^{2}}$$

Calculate -x^{3} to the power of 2 and get \left(x^{3}\right)^{2}.

$$\frac{-27x^{6}y^{3}z^{3}}{\left(x^{3}\right)^{2}y^{2}z^{2}}$$

Cancel out y^{2}z^{2} in both numerator and denominator.

$$\frac{-27yzx^{6}}{\left(x^{3}\right)^{2}}$$

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

$$\frac{-27yzx^{6}}{x^{6}}$$

Cancel out x^{6} in both numerator and denominator.

$$-27yz$$

Expand

$$-27yz$$

Solution Steps

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

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

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

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

Calculate -3 to the power of 3 and get -27.

$$\frac{-27x^{6}y^{3}z^{3}}{\left(\left(-x^{3}\right)yz\right)^{2}}$$

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

$$\frac{-27x^{6}y^{3}z^{3}}{\left(-x^{3}\right)^{2}y^{2}z^{2}}$$

Calculate -x^{3} to the power of 2 and get \left(x^{3}\right)^{2}.

$$\frac{-27x^{6}y^{3}z^{3}}{\left(x^{3}\right)^{2}y^{2}z^{2}}$$

Cancel out y^{2}z^{2} in both numerator and denominator.

$$\frac{-27yzx^{6}}{\left(x^{3}\right)^{2}}$$

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

$$\frac{-27yzx^{6}}{x^{6}}$$

Cancel out x^{6} in both numerator and denominator.

$$-27yz$$