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

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

Evaluate

$$\frac{16\left(xy\right)^{8}}{z^{6}}$$

Solution Steps

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

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

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

$$\frac{\left(4x^{4}y^{4}\right)^{2}}{z^{6}}$$

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

$$\frac{4^{2}\left(x^{4}\right)^{2}\left(y^{4}\right)^{2}}{z^{6}}$$

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

$$\frac{4^{2}x^{8}\left(y^{4}\right)^{2}}{z^{6}}$$

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

$$\frac{4^{2}x^{8}y^{8}}{z^{6}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16x^{8}y^{8}}{z^{6}}$$

Expand

$$\frac{16\left(xy\right)^{8}}{z^{6}}$$

Solution Steps

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

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

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

$$\frac{\left(4x^{4}y^{4}\right)^{2}}{z^{6}}$$

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

$$\frac{4^{2}\left(x^{4}\right)^{2}\left(y^{4}\right)^{2}}{z^{6}}$$

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

$$\frac{4^{2}x^{8}\left(y^{4}\right)^{2}}{z^{6}}$$

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

$$\frac{4^{2}x^{8}y^{8}}{z^{6}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16x^{8}y^{8}}{z^{6}}$$