Solve (frac{2x^{4}z^-4}{8x^3yz^2})^-3

$$( \frac { 2 x ^ { 4 } z ^ { - 4 } } { 8 x ^ { 3 } y z ^ { 2 } } ) ^ { - 3 }$$

Evaluate

$$64\times \left(\frac{y}{x}\right)^{3}z^{18}$$

Solution Steps

Cancel out 2x^{3} in both numerator and denominator.

$$\left(\frac{z^{-4}x}{4yz^{2}}\right)^{-3}$$

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

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

To raise \frac{x}{4yz^{6}} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(4yz^{6}\right)^{-3}.

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

To raise a power to another power, multiply the exponents. Multiply 6 and -3 to get -18.

$$\frac{x^{-3}}{4^{-3}y^{-3}z^{-18}}$$

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

$$\frac{x^{-3}}{\frac{1}{64}y^{-3}z^{-18}}$$

Expand

$$64\times \left(\frac{y}{x}\right)^{3}z^{18}$$

Solution Steps

Cancel out 2x^{3} in both numerator and denominator.

$$\left(\frac{z^{-4}x}{4yz^{2}}\right)^{-3}$$

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

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

To raise \frac{x}{4yz^{6}} to a power, raise both numerator and denominator to the power and then divide.

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

Expand \left(4yz^{6}\right)^{-3}.

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

To raise a power to another power, multiply the exponents. Multiply 6 and -3 to get -18.

$$\frac{x^{-3}}{4^{-3}y^{-3}z^{-18}}$$

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

$$\frac{x^{-3}}{\frac{1}{64}y^{-3}z^{-18}}$$