Solve (frac{x^{3}*x^{5}*y^8}{x^4*y^3})^5

$$( \frac { x ^ { 3 } \times x ^ { 5 } \times y ^ { 8 } } { x ^ { 4 } \times y ^ { 3 } } ) ^ { 5 }$$

Evaluate

$$x^{20}y^{25}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$\left(\frac{x^{8}y^{8}}{x^{4}y^{3}}\right)^{5}$$

Cancel out y^{3}x^{4} in both numerator and denominator.

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

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

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

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

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

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

$$x^{20}y^{25}$$

Expand

$$x^{20}y^{25}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 5 to get 8.

$$\left(\frac{x^{8}y^{8}}{x^{4}y^{3}}\right)^{5}$$

Cancel out y^{3}x^{4} in both numerator and denominator.

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

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

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

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

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

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

$$x^{20}y^{25}$$