Solve (y^2/xz)^3div(y^6z)

$$( \frac { y ^ { 2 } } { x z } ) ^ { 3 } \div ( y ^ { 6 } z )$$

Evaluate

$$\frac{1}{x^{3}z^{4}}$$

Solution Steps

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

$$\frac{\frac{\left(y^{2}\right)^{3}}{\left(xz\right)^{3}}}{y^{6}z}$$

Express \frac{\frac{\left(y^{2}\right)^{3}}{\left(xz\right)^{3}}}{y^{6}z} as a single fraction.

$$\frac{\left(y^{2}\right)^{3}}{\left(xz\right)^{3}y^{6}z}$$

Expand \left(xz\right)^{3}.

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

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

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

$$\frac{y^{6}}{x^{3}z^{4}y^{6}}$$

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

$$\frac{1}{x^{3}z^{4}}$$

Expand

$$\frac{1}{x^{3}z^{4}}$$

Solution Steps

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

$$\frac{\frac{\left(y^{2}\right)^{3}}{\left(xz\right)^{3}}}{y^{6}z}$$

Express \frac{\frac{\left(y^{2}\right)^{3}}{\left(xz\right)^{3}}}{y^{6}z} as a single fraction.

$$\frac{\left(y^{2}\right)^{3}}{\left(xz\right)^{3}y^{6}z}$$

Expand \left(xz\right)^{3}.

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

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

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

$$\frac{y^{6}}{x^{3}z^{4}y^{6}}$$

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

$$\frac{1}{x^{3}z^{4}}$$