Solve (3y^-3/4xz^-1)^-3]

$$( \frac { 3 y ^ { - 3 } } { 4 x z ^ { - 1 } } ) ^ { - 3 } ]$$

Evaluate

$$\frac{64\times \left(\frac{x}{z}\right)^{3}y^{9}}{27}$$

Solution Steps

To raise \frac{3y^{-3}}{4xz^{-1}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3y^{-3}\right)^{-3}}{\left(4xz^{-1}\right)^{-3}}$$

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

$$\frac{3^{-3}\left(y^{-3}\right)^{-3}}{\left(4xz^{-1}\right)^{-3}}$$

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

$$\frac{3^{-3}y^{9}}{\left(4xz^{-1}\right)^{-3}}$$

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

$$\frac{\frac{1}{27}y^{9}}{\left(4xz^{-1}\right)^{-3}}$$

Expand \left(4xz^{-1}\right)^{-3}.

$$\frac{\frac{1}{27}y^{9}}{4^{-3}x^{-3}\left(z^{-1}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -3 to get 3.

$$\frac{\frac{1}{27}y^{9}}{4^{-3}x^{-3}z^{3}}$$

Calculate 4 to the power of -3 and get \frac{1}{64}.

$$\frac{\frac{1}{27}y^{9}}{\frac{1}{64}x^{-3}z^{3}}$$

Expand

$$\frac{64\times \left(\frac{x}{z}\right)^{3}y^{9}}{27}$$

Solution Steps

To raise \frac{3y^{-3}}{4xz^{-1}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3y^{-3}\right)^{-3}}{\left(4xz^{-1}\right)^{-3}}$$

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

$$\frac{3^{-3}\left(y^{-3}\right)^{-3}}{\left(4xz^{-1}\right)^{-3}}$$

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

$$\frac{3^{-3}y^{9}}{\left(4xz^{-1}\right)^{-3}}$$

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

$$\frac{\frac{1}{27}y^{9}}{\left(4xz^{-1}\right)^{-3}}$$

Expand \left(4xz^{-1}\right)^{-3}.

$$\frac{\frac{1}{27}y^{9}}{4^{-3}x^{-3}\left(z^{-1}\right)^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -3 to get 3.

$$\frac{\frac{1}{27}y^{9}}{4^{-3}x^{-3}z^{3}}$$

Calculate 4 to the power of -3 and get \frac{1}{64}.

$$\frac{\frac{1}{27}y^{9}}{\frac{1}{64}x^{-3}z^{3}}$$