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

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

Evaluate

$$-\frac{27x^{9}}{y^{6}}$$

Solution Steps

Cancel out y^{2} in both numerator and denominator.

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

Calculate 3 to the power of 0 and get 1.

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

Anything divided by one gives itself.

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

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

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

To raise a power to another power, multiply the exponents. Multiply -3 and -3 to get 9.

$$\left(-\frac{1}{3}\right)^{-3}x^{9}\left(y^{2}\right)^{-3}$$

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

$$\left(-\frac{1}{3}\right)^{-3}x^{9}y^{-6}$$

Calculate -\frac{1}{3} to the power of -3 and get -27.

$$-27x^{9}y^{-6}$$

Expand

$$-\frac{27x^{9}}{y^{6}}$$

Solution Steps

Cancel out y^{2} in both numerator and denominator.

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

Calculate 3 to the power of 0 and get 1.

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

Anything divided by one gives itself.

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

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

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

To raise a power to another power, multiply the exponents. Multiply -3 and -3 to get 9.

$$\left(-\frac{1}{3}\right)^{-3}x^{9}\left(y^{2}\right)^{-3}$$

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

$$\left(-\frac{1}{3}\right)^{-3}x^{9}y^{-6}$$

Calculate -\frac{1}{3} to the power of -3 and get -27.

$$-27x^{9}y^{-6}$$