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

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

Evaluate

$$\frac{27x^{6}y^{12}}{z^{3}}$$

Solution Steps

To raise \frac{3x^{2}y^{4}}{z} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(3x^{2}y^{4}\right)^{3}.

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

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

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

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

$$\frac{3^{3}x^{6}y^{12}}{z^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27x^{6}y^{12}}{z^{3}}$$

Expand

$$\frac{27x^{6}y^{12}}{z^{3}}$$

Solution Steps

To raise \frac{3x^{2}y^{4}}{z} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(3x^{2}y^{4}\right)^{3}.

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

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

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

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

$$\frac{3^{3}x^{6}y^{12}}{z^{3}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27x^{6}y^{12}}{z^{3}}$$