Solve (5x^4y^5/2xy^4)^4

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

Evaluate

$$\frac{625y^{4}x^{12}}{16}$$

Solution Steps

Cancel out xy^{4} in both numerator and denominator.

$$\left(\frac{5yx^{3}}{2}\right)^{4}$$

To raise \frac{5yx^{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5yx^{3}\right)^{4}}{2^{4}}$$

Expand \left(5yx^{3}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{5^{4}y^{4}x^{12}}{2^{4}}$$

Calculate 5 to the power of 4 and get 625.

$$\frac{625y^{4}x^{12}}{2^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{625y^{4}x^{12}}{16}$$

Expand

$$\frac{625y^{4}x^{12}}{16}$$

Solution Steps

Cancel out xy^{4} in both numerator and denominator.

$$\left(\frac{5yx^{3}}{2}\right)^{4}$$

To raise \frac{5yx^{3}}{2} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5yx^{3}\right)^{4}}{2^{4}}$$

Expand \left(5yx^{3}\right)^{4}.

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

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$\frac{5^{4}y^{4}x^{12}}{2^{4}}$$

Calculate 5 to the power of 4 and get 625.

$$\frac{625y^{4}x^{12}}{2^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{625y^{4}x^{12}}{16}$$