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

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

Evaluate

$$y^{12}x^{30}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{\left(x^{6}y^{4}\right)^{5}}{y^{8}}$$

Expand \left(x^{6}y^{4}\right)^{5}.

$$\frac{\left(x^{6}\right)^{5}\left(y^{4}\right)^{5}}{y^{8}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 5 to get 30.

$$\frac{x^{30}\left(y^{4}\right)^{5}}{y^{8}}$$

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

$$\frac{x^{30}y^{20}}{y^{8}}$$

Cancel out y^{8} in both numerator and denominator.

$$y^{12}x^{30}$$

Expand

$$y^{12}x^{30}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{\left(x^{6}y^{4}\right)^{5}}{y^{8}}$$

Expand \left(x^{6}y^{4}\right)^{5}.

$$\frac{\left(x^{6}\right)^{5}\left(y^{4}\right)^{5}}{y^{8}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 5 to get 30.

$$\frac{x^{30}\left(y^{4}\right)^{5}}{y^{8}}$$

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

$$\frac{x^{30}y^{20}}{y^{8}}$$

Cancel out y^{8} in both numerator and denominator.

$$y^{12}x^{30}$$