Solve frac{(x^{2}y^{3})*(x^{4}y^{5})^5}{y^7*x^6y^6}

$$\frac { ( x ^ { 2 } y ^ { 3 } ) \cdot ( x ^ { 4 } y ^ { 5 } ) ^ { 5 } } { y ^ { 7 } \cdot x ^ { 6 } y ^ { 6 } }$$

Evaluate

$$y^{15}x^{16}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 6 to get 13.

$$\frac{x^{2}y^{3}\left(x^{4}y^{5}\right)^{5}}{y^{13}x^{6}}$$

Cancel out x^{2}y^{3} in both numerator and denominator.

$$\frac{\left(x^{4}y^{5}\right)^{5}}{x^{4}y^{10}}$$

Expand \left(x^{4}y^{5}\right)^{5}.

$$\frac{\left(x^{4}\right)^{5}\left(y^{5}\right)^{5}}{x^{4}y^{10}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$\frac{x^{20}\left(y^{5}\right)^{5}}{x^{4}y^{10}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 5 to get 25.

$$\frac{x^{20}y^{25}}{x^{4}y^{10}}$$

Cancel out x^{4}y^{10} in both numerator and denominator.

$$y^{15}x^{16}$$

Expand

$$y^{15}x^{16}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 6 to get 13.

$$\frac{x^{2}y^{3}\left(x^{4}y^{5}\right)^{5}}{y^{13}x^{6}}$$

Cancel out x^{2}y^{3} in both numerator and denominator.

$$\frac{\left(x^{4}y^{5}\right)^{5}}{x^{4}y^{10}}$$

Expand \left(x^{4}y^{5}\right)^{5}.

$$\frac{\left(x^{4}\right)^{5}\left(y^{5}\right)^{5}}{x^{4}y^{10}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 5 to get 20.

$$\frac{x^{20}\left(y^{5}\right)^{5}}{x^{4}y^{10}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 5 to get 25.

$$\frac{x^{20}y^{25}}{x^{4}y^{10}}$$

Cancel out x^{4}y^{10} in both numerator and denominator.

$$y^{15}x^{16}$$