Solve {left(12x^3y^4/9z^5right)}^2

$${ \left( \frac{ 12 { x }^{ 3 } { y }^{ 4 } }{ 9 { z }^{ 5 } } \right) }^{ 2 }$$

Evaluate

$$\frac{16x^{6}y^{8}}{9z^{10}}$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\left(\frac{4x^{3}y^{4}}{3z^{5}}\right)^{2}$$

To raise \frac{4x^{3}y^{4}}{3z^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(4x^{3}y^{4}\right)^{2}}{\left(3z^{5}\right)^{2}}$$

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

$$\frac{4^{2}\left(x^{3}\right)^{2}\left(y^{4}\right)^{2}}{\left(3z^{5}\right)^{2}}$$

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

$$\frac{4^{2}x^{6}\left(y^{4}\right)^{2}}{\left(3z^{5}\right)^{2}}$$

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

$$\frac{4^{2}x^{6}y^{8}}{\left(3z^{5}\right)^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16x^{6}y^{8}}{\left(3z^{5}\right)^{2}}$$

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

$$\frac{16x^{6}y^{8}}{3^{2}\left(z^{5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{16x^{6}y^{8}}{3^{2}z^{10}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{16x^{6}y^{8}}{9z^{10}}$$

Expand

$$\frac{16x^{6}y^{8}}{9z^{10}}$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\left(\frac{4x^{3}y^{4}}{3z^{5}}\right)^{2}$$

To raise \frac{4x^{3}y^{4}}{3z^{5}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(4x^{3}y^{4}\right)^{2}}{\left(3z^{5}\right)^{2}}$$

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

$$\frac{4^{2}\left(x^{3}\right)^{2}\left(y^{4}\right)^{2}}{\left(3z^{5}\right)^{2}}$$

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

$$\frac{4^{2}x^{6}\left(y^{4}\right)^{2}}{\left(3z^{5}\right)^{2}}$$

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

$$\frac{4^{2}x^{6}y^{8}}{\left(3z^{5}\right)^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16x^{6}y^{8}}{\left(3z^{5}\right)^{2}}$$

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

$$\frac{16x^{6}y^{8}}{3^{2}\left(z^{5}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{16x^{6}y^{8}}{3^{2}z^{10}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{16x^{6}y^{8}}{9z^{10}}$$