Solve frac{(5x^{7}y^7)^2}{10x^9y^3}

$$\frac { ( 5 x ^ { 7 } y ^ { 7 } ) ^ { 2 } } { 10 x ^ { 9 } y ^ { 3 } }$$

Evaluate

$$\frac{5x^{5}y^{11}}{2}$$

Solution Steps

Expand \left(5x^{7}y^{7}\right)^{2}.

$$\frac{5^{2}\left(x^{7}\right)^{2}\left(y^{7}\right)^{2}}{10x^{9}y^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{5^{2}x^{14}\left(y^{7}\right)^{2}}{10x^{9}y^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{5^{2}x^{14}y^{14}}{10x^{9}y^{3}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25x^{14}y^{14}}{10x^{9}y^{3}}$$

Cancel out 5y^{3}x^{9} in both numerator and denominator.

$$\frac{5x^{5}y^{11}}{2}$$

Expand

$$\frac{5x^{5}y^{11}}{2}$$

Solution Steps

Expand \left(5x^{7}y^{7}\right)^{2}.

$$\frac{5^{2}\left(x^{7}\right)^{2}\left(y^{7}\right)^{2}}{10x^{9}y^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{5^{2}x^{14}\left(y^{7}\right)^{2}}{10x^{9}y^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\frac{5^{2}x^{14}y^{14}}{10x^{9}y^{3}}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{25x^{14}y^{14}}{10x^{9}y^{3}}$$

Cancel out 5y^{3}x^{9} in both numerator and denominator.

$$\frac{5x^{5}y^{11}}{2}$$