Solve C_{5}(x/3)^5(9y)^5

$$C _ { 5 } ( \frac { x } { 3 } ) ^ { 5 } ( 9 y ) ^ { 5 }$$

Evaluate

$$243C_{5}\left(xy\right)^{5}$$

Solution Steps

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

$$C_{5}\times \frac{x^{5}}{3^{5}}\times \left(9y\right)^{5}$$

Expand \left(9y\right)^{5}.

$$C_{5}\times \frac{x^{5}}{3^{5}}\times 9^{5}y^{5}$$

Calculate 9 to the power of 5 and get 59049.

$$C_{5}\times \frac{x^{5}}{3^{5}}\times 59049y^{5}$$

Express C_{5}\times \frac{x^{5}}{3^{5}} as a single fraction.

$$\frac{C_{5}x^{5}}{3^{5}}\times 59049y^{5}$$

Express \frac{C_{5}x^{5}}{3^{5}}\times 59049 as a single fraction.

$$\frac{C_{5}x^{5}\times 59049}{3^{5}}y^{5}$$

Express \frac{C_{5}x^{5}\times 59049}{3^{5}}y^{5} as a single fraction.

$$\frac{C_{5}x^{5}\times 59049y^{5}}{3^{5}}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{C_{5}x^{5}\times 59049y^{5}}{243}$$

Divide C_{5}x^{5}\times 59049y^{5} by 243 to get C_{5}x^{5}\times 243y^{5}.

$$C_{5}x^{5}\times 243y^{5}$$

Expand

$$243C_{5}\left(xy\right)^{5}$$

Solution Steps

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

$$C_{5}\times \frac{x^{5}}{3^{5}}\times \left(9y\right)^{5}$$

Expand \left(9y\right)^{5}.

$$C_{5}\times \frac{x^{5}}{3^{5}}\times 9^{5}y^{5}$$

Calculate 9 to the power of 5 and get 59049.

$$C_{5}\times \frac{x^{5}}{3^{5}}\times 59049y^{5}$$

Express C_{5}\times \frac{x^{5}}{3^{5}} as a single fraction.

$$\frac{C_{5}x^{5}}{3^{5}}\times 59049y^{5}$$

Express \frac{C_{5}x^{5}}{3^{5}}\times 59049 as a single fraction.

$$\frac{C_{5}x^{5}\times 59049}{3^{5}}y^{5}$$

Express \frac{C_{5}x^{5}\times 59049}{3^{5}}y^{5} as a single fraction.

$$\frac{C_{5}x^{5}\times 59049y^{5}}{3^{5}}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{C_{5}x^{5}\times 59049y^{5}}{243}$$

Divide C_{5}x^{5}\times 59049y^{5} by 243 to get C_{5}x^{5}\times 243y^{5}.

$$C_{5}x^{5}\times 243y^{5}$$