Solve (3x^2y/y^3)^5

$$( \frac { 3 x ^ { 2 } y } { y ^ { 3 } } ) ^ { 5 }$$

Evaluate

$$243\times \left(\frac{x}{y}\right)^{10}$$

Solution Steps

Cancel out y in both numerator and denominator.

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

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

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

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

$$\frac{\left(3x^{2}\right)^{5}}{y^{10}}$$

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

$$\frac{3^{5}\left(x^{2}\right)^{5}}{y^{10}}$$

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

$$\frac{3^{5}x^{10}}{y^{10}}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{243x^{10}}{y^{10}}$$

Expand

$$243\times \left(\frac{x}{y}\right)^{10}$$

Solution Steps

Cancel out y in both numerator and denominator.

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

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

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

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

$$\frac{\left(3x^{2}\right)^{5}}{y^{10}}$$

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

$$\frac{3^{5}\left(x^{2}\right)^{5}}{y^{10}}$$

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

$$\frac{3^{5}x^{10}}{y^{10}}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{243x^{10}}{y^{10}}$$