Solve (5zc^5/9z^2c^3)^3

$$( \frac { 5 z c ^ { 5 } } { 9 z ^ { 2 } c ^ { 3 } } ) ^ { 3 }$$

Evaluate

$$\frac{125c^{6}}{729z^{3}}$$

Solution Steps

Cancel out zc^{3} in both numerator and denominator.

$$\left(\frac{5c^{2}}{9z}\right)^{3}$$

To raise \frac{5c^{2}}{9z} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5c^{2}\right)^{3}}{\left(9z\right)^{3}}$$

Expand \left(5c^{2}\right)^{3}.

$$\frac{5^{3}\left(c^{2}\right)^{3}}{\left(9z\right)^{3}}$$

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

$$\frac{5^{3}c^{6}}{\left(9z\right)^{3}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{125c^{6}}{\left(9z\right)^{3}}$$

Expand \left(9z\right)^{3}.

$$\frac{125c^{6}}{9^{3}z^{3}}$$

Calculate 9 to the power of 3 and get 729.

$$\frac{125c^{6}}{729z^{3}}$$

Expand

$$\frac{125c^{6}}{729z^{3}}$$

Solution Steps

Cancel out zc^{3} in both numerator and denominator.

$$\left(\frac{5c^{2}}{9z}\right)^{3}$$

To raise \frac{5c^{2}}{9z} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5c^{2}\right)^{3}}{\left(9z\right)^{3}}$$

Expand \left(5c^{2}\right)^{3}.

$$\frac{5^{3}\left(c^{2}\right)^{3}}{\left(9z\right)^{3}}$$

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

$$\frac{5^{3}c^{6}}{\left(9z\right)^{3}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{125c^{6}}{\left(9z\right)^{3}}$$

Expand \left(9z\right)^{3}.

$$\frac{125c^{6}}{9^{3}z^{3}}$$

Calculate 9 to the power of 3 and get 729.

$$\frac{125c^{6}}{729z^{3}}$$