Solve {left(6x^-5y^-2z^3/2xy^-2{z^-3}right)}^-3

$${ \left( \frac{ 6 { x }^{ -5 } { y }^{ -2 } { z }^{ 3 } }{ 2x { y }^{ -2 } { z }^{ -3 } } \right) }^{ -3 }$$

Evaluate

$$\frac{\left(\frac{x}{z}\right)^{18}}{27}$$

Solution Steps

Cancel out 2y^{-2} in both numerator and denominator.

$$\left(\frac{3x^{-5}z^{3}}{z^{-3}x}\right)^{-3}$$

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

$$\left(\frac{3x^{-5}z^{6}}{x}\right)^{-3}$$

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

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

To raise \frac{3z^{6}}{x^{6}} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{\left(3z^{6}\right)^{-3}}{x^{-18}}$$

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

$$\frac{3^{-3}\left(z^{6}\right)^{-3}}{x^{-18}}$$

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

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

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

$$\frac{\frac{1}{27}z^{-18}}{x^{-18}}$$

Expand

$$\frac{\left(\frac{x}{z}\right)^{18}}{27}$$

Solution Steps

Cancel out 2y^{-2} in both numerator and denominator.

$$\left(\frac{3x^{-5}z^{3}}{z^{-3}x}\right)^{-3}$$

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

$$\left(\frac{3x^{-5}z^{6}}{x}\right)^{-3}$$

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

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

To raise \frac{3z^{6}}{x^{6}} to a power, raise both numerator and denominator to the power and then divide.

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

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

$$\frac{\left(3z^{6}\right)^{-3}}{x^{-18}}$$

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

$$\frac{3^{-3}\left(z^{6}\right)^{-3}}{x^{-18}}$$

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

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

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

$$\frac{\frac{1}{27}z^{-18}}{x^{-18}}$$