Solve {left(3x^2y^4/z^3right)}^4

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

Evaluate

$$\frac{81x^{8}y^{16}}{z^{12}}$$

Solution Steps

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

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

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

$$\frac{\left(3x^{2}y^{4}\right)^{4}}{z^{12}}$$

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

$$\frac{3^{4}\left(x^{2}\right)^{4}\left(y^{4}\right)^{4}}{z^{12}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{3^{4}x^{8}\left(y^{4}\right)^{4}}{z^{12}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\frac{3^{4}x^{8}y^{16}}{z^{12}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{81x^{8}y^{16}}{z^{12}}$$

Expand

$$\frac{81x^{8}y^{16}}{z^{12}}$$

Solution Steps

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

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

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

$$\frac{\left(3x^{2}y^{4}\right)^{4}}{z^{12}}$$

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

$$\frac{3^{4}\left(x^{2}\right)^{4}\left(y^{4}\right)^{4}}{z^{12}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\frac{3^{4}x^{8}\left(y^{4}\right)^{4}}{z^{12}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\frac{3^{4}x^{8}y^{16}}{z^{12}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{81x^{8}y^{16}}{z^{12}}$$