Solve (x^3y^7/5z)^4

$$( \frac { x ^ { 3 } y ^ { 7 } } { 5 z } ) ^ { 4 }$$

Evaluate

$$\frac{x^{12}y^{28}}{625z^{4}}$$

Solution Steps

To raise \frac{x^{3}y^{7}}{5z} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x^{3}y^{7}\right)^{4}}{\left(5z\right)^{4}}$$

Expand \left(x^{3}y^{7}\right)^{4}.

$$\frac{\left(x^{3}\right)^{4}\left(y^{7}\right)^{4}}{\left(5z\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{x^{12}\left(y^{7}\right)^{4}}{\left(5z\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 4 to get 28.

$$\frac{x^{12}y^{28}}{\left(5z\right)^{4}}$$

Expand \left(5z\right)^{4}.

$$\frac{x^{12}y^{28}}{5^{4}z^{4}}$$

Calculate 5 to the power of 4 and get 625.

$$\frac{x^{12}y^{28}}{625z^{4}}$$

Expand

$$\frac{x^{12}y^{28}}{625z^{4}}$$

Solution Steps

To raise \frac{x^{3}y^{7}}{5z} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x^{3}y^{7}\right)^{4}}{\left(5z\right)^{4}}$$

Expand \left(x^{3}y^{7}\right)^{4}.

$$\frac{\left(x^{3}\right)^{4}\left(y^{7}\right)^{4}}{\left(5z\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{x^{12}\left(y^{7}\right)^{4}}{\left(5z\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 4 to get 28.

$$\frac{x^{12}y^{28}}{\left(5z\right)^{4}}$$

Expand \left(5z\right)^{4}.

$$\frac{x^{12}y^{28}}{5^{4}z^{4}}$$

Calculate 5 to the power of 4 and get 625.

$$\frac{x^{12}y^{28}}{625z^{4}}$$