Solve (x^-3/3y^-1)^-2

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

Evaluate

$$\frac{9x^{6}}{y^{2}}$$

Solution Steps

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

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

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

$$\frac{x^{6}}{\left(3y^{-1}\right)^{-2}}$$

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

$$\frac{x^{6}}{3^{-2}\left(y^{-1}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -2 to get 2.

$$\frac{x^{6}}{3^{-2}y^{2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{x^{6}}{\frac{1}{9}y^{2}}$$

Expand

$$\frac{9x^{6}}{y^{2}}$$

Solution Steps

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

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

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

$$\frac{x^{6}}{\left(3y^{-1}\right)^{-2}}$$

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

$$\frac{x^{6}}{3^{-2}\left(y^{-1}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -2 to get 2.

$$\frac{x^{6}}{3^{-2}y^{2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{x^{6}}{\frac{1}{9}y^{2}}$$