Solve {left(3xy^3/z^3right)}^2

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

Evaluate

$$9\times \left(\frac{y}{z}\right)^{6}x^{2}$$

Solution Steps

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

$$\frac{\left(3xy^{3}\right)^{2}}{\left(z^{3}\right)^{2}}$$

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

$$\frac{\left(3xy^{3}\right)^{2}}{z^{6}}$$

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

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

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

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

Calculate 3 to the power of 2 and get 9.

$$\frac{9x^{2}y^{6}}{z^{6}}$$

Expand

$$9\times \left(\frac{y}{z}\right)^{6}x^{2}$$

Solution Steps

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

$$\frac{\left(3xy^{3}\right)^{2}}{\left(z^{3}\right)^{2}}$$

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

$$\frac{\left(3xy^{3}\right)^{2}}{z^{6}}$$

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

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

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

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

Calculate 3 to the power of 2 and get 9.

$$\frac{9x^{2}y^{6}}{z^{6}}$$