Solve (4x^5y/xy^2)^3

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

Evaluate

$$\frac{64x^{12}}{y^{3}}$$

Solution Steps

Cancel out xy in both numerator and denominator.

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

To raise \frac{4x^{4}}{y} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

$$\frac{4^{3}x^{12}}{y^{3}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64x^{12}}{y^{3}}$$

Expand

$$\frac{64x^{12}}{y^{3}}$$

Solution Steps

Cancel out xy in both numerator and denominator.

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

To raise \frac{4x^{4}}{y} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

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

$$\frac{4^{3}x^{12}}{y^{3}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64x^{12}}{y^{3}}$$