Solve (frac{(4x^{2}y^{3})^0}{-3x^-1y^2})^3

$$( \frac { ( 4 x ^ { 2 } y ^ { 3 } ) ^ { 0 } } { - 3 x ^ { - 1 } y ^ { 2 } } ) ^ { 3 }$$

Evaluate

$$-\frac{x^{3}}{27y^{6}}$$

Solution Steps

Calculate 4x^{2}y^{3} to the power of 0 and get 1.

$$\left(\frac{1}{-3x^{-1}y^{2}}\right)^{3}$$

To raise \frac{1}{-3x^{-1}y^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{3}}{\left(-3x^{-1}y^{2}\right)^{3}}$$

Calculate 1 to the power of 3 and get 1.

$$\frac{1}{\left(-3x^{-1}y^{2}\right)^{3}}$$

Expand \left(-3x^{-1}y^{2}\right)^{3}.

$$\frac{1}{\left(-3\right)^{3}\left(x^{-1}\right)^{3}\left(y^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

$$\frac{1}{\left(-3\right)^{3}x^{-3}\left(y^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{1}{\left(-3\right)^{3}x^{-3}y^{6}}$$

Calculate -3 to the power of 3 and get -27.

$$\frac{1}{-27x^{-3}y^{6}}$$

Expand

$$-\frac{x^{3}}{27y^{6}}$$

Solution Steps

Calculate 4x^{2}y^{3} to the power of 0 and get 1.

$$\left(\frac{1}{-3x^{-1}y^{2}}\right)^{3}$$

To raise \frac{1}{-3x^{-1}y^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{3}}{\left(-3x^{-1}y^{2}\right)^{3}}$$

Calculate 1 to the power of 3 and get 1.

$$\frac{1}{\left(-3x^{-1}y^{2}\right)^{3}}$$

Expand \left(-3x^{-1}y^{2}\right)^{3}.

$$\frac{1}{\left(-3\right)^{3}\left(x^{-1}\right)^{3}\left(y^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

$$\frac{1}{\left(-3\right)^{3}x^{-3}\left(y^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{1}{\left(-3\right)^{3}x^{-3}y^{6}}$$

Calculate -3 to the power of 3 and get -27.

$$\frac{1}{-27x^{-3}y^{6}}$$