Solve (3x^8/x^4y^4)^2

$$( \frac { 3 x ^ { 8 } } { x ^ { 4 } y ^ { 4 } } ) ^ { 2 }$$

Evaluate

$$9\times \left(\frac{x}{y}\right)^{8}$$

Solution Steps

Cancel out x^{4} in both numerator and denominator.

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

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

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

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

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

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

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

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

$$\frac{3^{2}x^{8}}{y^{8}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9x^{8}}{y^{8}}$$

Expand

$$9\times \left(\frac{x}{y}\right)^{8}$$

Solution Steps

Cancel out x^{4} in both numerator and denominator.

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

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

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

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

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

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

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

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

$$\frac{3^{2}x^{8}}{y^{8}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9x^{8}}{y^{8}}$$