Solve frac{(frac{x^{2}y}{z})^3*(z/x^3)}{(y)^13*(x)^2}

$$\frac { ( \frac { x ^ { 2 } y } { z } ) ^ { 3 } \cdot ( \frac { z } { x ^ { 3 } } ) } { ( y ) ^ { 13 } \cdot ( x ) ^ { 2 } }$$

Evaluate

$$\frac{x}{z^{2}y^{10}}$$

Solution Steps

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

$$\frac{\frac{\left(x^{2}y\right)^{3}}{z^{3}}\times \frac{z}{x^{3}}}{y^{13}x^{2}}$$

Multiply \frac{\left(x^{2}y\right)^{3}}{z^{3}} times \frac{z}{x^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\left(x^{2}y\right)^{3}z}{z^{3}x^{3}}}{y^{13}x^{2}}$$

Cancel out z in both numerator and denominator.

$$\frac{\frac{\left(yx^{2}\right)^{3}}{z^{2}x^{3}}}{y^{13}x^{2}}$$

Express \frac{\frac{\left(yx^{2}\right)^{3}}{z^{2}x^{3}}}{y^{13}x^{2}} as a single fraction.

$$\frac{\left(yx^{2}\right)^{3}}{z^{2}x^{3}y^{13}x^{2}}$$

Expand \left(yx^{2}\right)^{3}.

$$\frac{y^{3}\left(x^{2}\right)^{3}}{z^{2}x^{3}y^{13}x^{2}}$$

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

$$\frac{y^{3}x^{6}}{z^{2}x^{3}y^{13}x^{2}}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{y^{3}x^{6}}{z^{2}x^{5}y^{13}}$$

Cancel out y^{3}x^{5} in both numerator and denominator.

$$\frac{x}{z^{2}y^{10}}$$

Expand

$$\frac{x}{z^{2}y^{10}}$$

Solution Steps

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

$$\frac{\frac{\left(x^{2}y\right)^{3}}{z^{3}}\times \frac{z}{x^{3}}}{y^{13}x^{2}}$$

Multiply \frac{\left(x^{2}y\right)^{3}}{z^{3}} times \frac{z}{x^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{\left(x^{2}y\right)^{3}z}{z^{3}x^{3}}}{y^{13}x^{2}}$$

Cancel out z in both numerator and denominator.

$$\frac{\frac{\left(yx^{2}\right)^{3}}{z^{2}x^{3}}}{y^{13}x^{2}}$$

Express \frac{\frac{\left(yx^{2}\right)^{3}}{z^{2}x^{3}}}{y^{13}x^{2}} as a single fraction.

$$\frac{\left(yx^{2}\right)^{3}}{z^{2}x^{3}y^{13}x^{2}}$$

Expand \left(yx^{2}\right)^{3}.

$$\frac{y^{3}\left(x^{2}\right)^{3}}{z^{2}x^{3}y^{13}x^{2}}$$

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

$$\frac{y^{3}x^{6}}{z^{2}x^{3}y^{13}x^{2}}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{y^{3}x^{6}}{z^{2}x^{5}y^{13}}$$

Cancel out y^{3}x^{5} in both numerator and denominator.

$$\frac{x}{z^{2}y^{10}}$$