Solve frac{(3x^{5}y^5)^3}{3x^3y^11}

$$\frac { ( 3 x ^ { 5 } y ^ { 5 } ) ^ { 3 } } { 3 x ^ { 3 } y ^ { 11 } }$$

Evaluate

$$9y^{4}x^{12}$$

Solution Steps

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

$$\frac{3^{3}\left(x^{5}\right)^{3}\left(y^{5}\right)^{3}}{3x^{3}y^{11}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{3^{3}x^{15}\left(y^{5}\right)^{3}}{3x^{3}y^{11}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{3^{3}x^{15}y^{15}}{3x^{3}y^{11}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27x^{15}y^{15}}{3x^{3}y^{11}}$$

Cancel out 3x^{3}y^{11} in both numerator and denominator.

$$9y^{4}x^{12}$$

Expand

$$9y^{4}x^{12}$$

Solution Steps

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

$$\frac{3^{3}\left(x^{5}\right)^{3}\left(y^{5}\right)^{3}}{3x^{3}y^{11}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{3^{3}x^{15}\left(y^{5}\right)^{3}}{3x^{3}y^{11}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 3 to get 15.

$$\frac{3^{3}x^{15}y^{15}}{3x^{3}y^{11}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27x^{15}y^{15}}{3x^{3}y^{11}}$$

Cancel out 3x^{3}y^{11} in both numerator and denominator.

$$9y^{4}x^{12}$$