Solve {left(x^-6y/xy^2right)}^-3

$${ \left( \frac{ { x }^{ -6 } y }{ x { y }^{ 2 } } \right) }^{ -3 }$$

Evaluate

$$y^{3}x^{21}$$

Solution Steps

Cancel out y in both numerator and denominator.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\left(\frac{1}{yx^{7}}\right)^{-3}$$

To raise \frac{1}{yx^{7}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{-3}}{\left(yx^{7}\right)^{-3}}$$

Calculate 1 to the power of -3 and get 1.

$$\frac{1}{\left(yx^{7}\right)^{-3}}$$

Expand \left(yx^{7}\right)^{-3}.

$$\frac{1}{y^{-3}\left(x^{7}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -3 to get -21.

$$\frac{1}{y^{-3}x^{-21}}$$

Expand

$$y^{3}x^{21}$$

Solution Steps

Cancel out y in both numerator and denominator.

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

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\left(\frac{1}{yx^{7}}\right)^{-3}$$

To raise \frac{1}{yx^{7}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{-3}}{\left(yx^{7}\right)^{-3}}$$

Calculate 1 to the power of -3 and get 1.

$$\frac{1}{\left(yx^{7}\right)^{-3}}$$

Expand \left(yx^{7}\right)^{-3}.

$$\frac{1}{y^{-3}\left(x^{7}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 7 and -3 to get -21.

$$\frac{1}{y^{-3}x^{-21}}$$