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

$$-\frac{1}{27y^{6}x^{9}}$$

Solution Steps

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

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

Calculate 3 to the power of 1 and get 3.

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

Calculate 3 to the power of 0 and get 1.

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

Anything divided by one gives itself.

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

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

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

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

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

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

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

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

$$-\frac{1}{27}y^{-6}x^{-9}$$

Expand

$$-\frac{1}{27y^{6}x^{9}}$$

Solution Steps

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

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

Calculate 3 to the power of 1 and get 3.

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

Calculate 3 to the power of 0 and get 1.

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

Anything divided by one gives itself.

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

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

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

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

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

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

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

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

$$-\frac{1}{27}y^{-6}x^{-9}$$