Solve frac{(6x^{-3}y^-3)^-3}{3x^4y^4}

$$\frac { ( 6 x ^ { - 3 } y ^ { - 3 } ) ^ { - 3 } } { 3 x ^ { 4 } y ^ { 4 } }$$

Evaluate

$$\frac{\left(xy\right)^{5}}{648}$$

Solution Steps

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

$$\frac{6^{-3}\left(x^{-3}\right)^{-3}\left(y^{-3}\right)^{-3}}{3x^{4}y^{4}}$$

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

$$\frac{6^{-3}x^{9}\left(y^{-3}\right)^{-3}}{3x^{4}y^{4}}$$

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

$$\frac{6^{-3}x^{9}y^{9}}{3x^{4}y^{4}}$$

Calculate 6 to the power of -3 and get \frac{1}{216}.

$$\frac{\frac{1}{216}x^{9}y^{9}}{3x^{4}y^{4}}$$

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

$$\frac{\frac{1}{216}x^{5}y^{5}}{3}$$

Divide \frac{1}{216}x^{5}y^{5} by 3 to get \frac{1}{648}x^{5}y^{5}.

$$\frac{1}{648}x^{5}y^{5}$$

Expand

$$\frac{\left(xy\right)^{5}}{648}$$

Solution Steps

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

$$\frac{6^{-3}\left(x^{-3}\right)^{-3}\left(y^{-3}\right)^{-3}}{3x^{4}y^{4}}$$

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

$$\frac{6^{-3}x^{9}\left(y^{-3}\right)^{-3}}{3x^{4}y^{4}}$$

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

$$\frac{6^{-3}x^{9}y^{9}}{3x^{4}y^{4}}$$

Calculate 6 to the power of -3 and get \frac{1}{216}.

$$\frac{\frac{1}{216}x^{9}y^{9}}{3x^{4}y^{4}}$$

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

$$\frac{\frac{1}{216}x^{5}y^{5}}{3}$$

Divide \frac{1}{216}x^{5}y^{5} by 3 to get \frac{1}{648}x^{5}y^{5}.

$$\frac{1}{648}x^{5}y^{5}$$