Solve (x/y)^4(y^2x/z)^3

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

Evaluate

$$\frac{y^{2}x^{7}}{z^{3}}$$

Solution Steps

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

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

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

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

Multiply \frac{x^{4}}{y^{4}} times \frac{\left(y^{2}x\right)^{3}}{z^{3}} by multiplying numerator times numerator and denominator times denominator.

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{x^{7}y^{6}}{y^{4}z^{3}}$$

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

$$\frac{y^{2}x^{7}}{z^{3}}$$

Expand

$$\frac{y^{2}x^{7}}{z^{3}}$$

Solution Steps

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

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

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

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

Multiply \frac{x^{4}}{y^{4}} times \frac{\left(y^{2}x\right)^{3}}{z^{3}} by multiplying numerator times numerator and denominator times denominator.

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{x^{7}y^{6}}{y^{4}z^{3}}$$

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

$$\frac{y^{2}x^{7}}{z^{3}}$$